Ćwiczenia do wykladu - Topologia I, Z.Szafraniec, UG
Pełen tekst
(2)
(3)
(4) !#" $&% ('*) % ,+-) % (. / 0!13254769-8 :#9=; < 0!1 9=< 6!>@?A2547BDC-E < 0 C-E!B 9=; <@F 0!1 9=< >@?G1 9=< E!B < >2H 0!1 9=< >@?G1 9=< E!BI2KJLBMJ <ON ?G1QPMR 9 EPMJLBCK132 9 CK0SBD> 9F 2UTL4VPXWYG2KH 6S2 F 2H TXZ!Y < 4[?\PMRA]^0!1 9=< >@?G1 9=< E!BI2KRA]`_ aKb.ced[f :!g hjilknmMo dqp iLrsm p tXb.c N 6!Cu4vC-YDEP 9=w B5K8C 1 x |a g hjilknmMo dyz {}. F@< =9 ; < YDB i d m F@< 9=; < DY B i d~ m. h J < ?G1QPXTU2=UQ o Mb.ced[f kVi d hji3kGi oOkvm d hm(3knm o 2 o&g hjilknmMo d iLrm Vd hji.rsm(@o . hji rsm o h J < ?G1QPXTU2OX(O*U o wo&g hjilknmMo dqp irm( p p i rsm p h J < ?G1QPXTU2 Uu¢U¡ UU o Ro p mp F@< 9=; < YDB i d m( g hjilknmMo d z {x p ii p r p irm( p p m p 4£0!1 9=< R=B¤47EPMJ4VPX0 2K6MTXZ h J < ?G1QPXTU2L¥G¦uOU o 6 o&g hjilknmMo d J 2¨§ h p i.rsm( p k p i rsm p o h J < ?G1QPXTU2Lu¥©-¡ ¤ªn¦5«*¬XU® o <¨o rsm F@< 9=; < YDB 0SZ!EMT(?\P il:Mm CK132 9°¯ >2±H 47>Q0²-8C ³YDYDBDE!BDCu4 < g hjilknmMo d z {x iL i m 4´0!1 9=< R=B¤47EPMJ4VPX0 2K6MTXZ h J < ?G1QPXTU2LU-µ¶=U o · b.ced[fª¸ :!i d hjik5¹5¹5¹*kni ¸ oOk!m d hm( k5¹5¹5¹Oknm ¸ o g hjilknmMo d iLrsm vd º ¸»µ¼ hji » rsm » o h J < ?G1QPXTU2^OX(O*U o.
(5)
(6) !"$#
(7) %'&()+* *,%*-. /*(01 /* " 324 5. 6Xb.ced[f87. f 7 :!ilk!m:9 ; rsm @F < 9=; < YDB 0SZ!EMT(?\P il:Mm CK132 9&¯ >2 H 47>Q0²-8C ³YDYDBDE!BDCu4 < g hjilknmMo dyz {x iª 4 0!1 9=< R=B¤47EPMJ4VPX0 2K6MTXZ i m £. h J < G? 1QPXTU2V¶5=¦ < o >Mb.c d ?8@ | k a
(8) A N 9=w B5K8C 1 1 9=< R 9 P47BD>@?\PMRA]CBZ!EMTR F B7R=BG2UH W³Y¤PMRA] ES2sC6!R=BDEMTXZ @ | k
(9) a A 2 o&g h D k EMo d J 2¨§!FGIHJG p D hji orKEhji o p d L F p D hji orMEhji o p g(i wo&g h D k EMo N b O B < RA] h c k ow < H 6 9 B < 0!1 9=< >@?G1 9=< E!BG2 H Z!E!CK1GJLCu4V2KE¢2 H b /0!13254769-8 : 9=; < BZ!EMTR F 2 g hjilknmMo d iLrm F@< >@?7J < ?G1QPXTU2&4 csb PM b O B < RA] h c kGgM\oOk,h QkGg ow < H 6¢2 H 0!1 9=< >@?G1 9=< E!BI2KJLBJ < ?G1QPMR 9 EPMJLB bRO B < RA] c T Q Wr V f _ S Ak S _ U 2 o S *hnhjiGknm(QoOk¨hji knm ono d gMOhji3kGi o g hm(3knm oO: wo S hnhjiGknm(QoOk¨hjinknm ono d gMOhji3kGi o . g hm(3knm o b /0!13254769-8 :.9=; < S Ak S >2°H J < ?G1QPXTU2KJLBES2 X c T Q Zb Y CKTU2 9-; :9=; < TU2 9 ; 6S2 TXZ!YI2 H TXZ!Y@< H [ ]h \ F k ^ o _+a h W6 9 B b [ ]h \ F k ^U@o _`±9 2547B < 132 0 < 47E¢2 < \ F 9 c T QL: ^Udc | :^ c | oO: B`ES2C6X4²1 U8C ? b eM b f 6!Cu4vC6!E!B F*:9=; < 6!BI2KJ [ hjilk^-odg t ^ b a | b f 6!Cu4vC6!E!B F*:9=; < TU2 9 ; 6S2±TXZ!YI2 F@< >@? 9=w BDCK1 < J CU?\4V2U1Q?\PMJ b 2 H h | N a hTU2 9 ; 6XP 9=w B5K8C 1 F@< >@? a-aKb f 6!Cu4vC6!E!B F*:L9=; < 4 0!1 9=< >@?G1 9=< E!B 9 J < ?G1QPXT i CU?\4V2U1Q?\P b autXb j ?K8C 1 < 9=<°9=w BDCK1 U8C 4 2 olk n d m hjilknmMoo9 f p i m q p · r : d m hjilknmMdo 9 f p i m c · r : wo [ s a R o ?n d m hjilknmMdo 9 f p H t a v uw g a r : 6 y d m hjilknmMdo 9 f p | g { o x n i z ak | g : m g ar: d m hjilk | do 9 f p | z { <¨y o | n i z ar >2 H CU?\4V2U1Q? <h C6M0 b 6!C-JªTXE!B@< H ? <-: CKW-132KE!BDR 9 C-E <¨o b.
(10)
(11) !"$#
(12) %'&()+* *,%*-. /*(01 /* " 324. a5Mbf 6!Cu4vC6!E!B F*:9=; < >QTC!8E R 9 C-ES2V>nZ!J 2 9=w BDCK1 U8C 4s6!C-JªTXE!B@< H ?\PMRA] F@< >@? 9=w BDCK1 < J 6!C-JªTXE!B@< H ?\PMJ b a · b Y CKTU2 9 ; 0!1 9 PXTXYI³ 2K6 9=w BDCK1GZ0!1 9=< YDBDR 9 2KYDE < WC : T(?K8C 1QPE!B <F@< >@?76!C-JªTXE!B@< H ?\P b a6Xb O B < RA] k c w < H 6 9 B < ?A2UTXBDJ 9=w BDCK1 < J :9=; <. . ? < 6XP. k
(13). 9 k. 9 k. F@< 9=; < YDB. !^.c. d~
(14). [ h k^Oo. |. dnm. k. ?3C [. h k ^ t o. a/>Mb < 9=; < YDB N CU?\4V2U1Q?\P : N 6!C-JªTXE!B@< H ?\P : ?3C F@< >@?²6!C-JªTXE!B@< H ?\P b. r¹. h
(15) ¨k ^t o d ¹ F@< >@?CU?\4V2U1Q?\P°CK132 9 [. .
(16) ! "! $(# .&% + '( ( &% (- ) % "! % " a N b f 6!Cu4vC6!E!B F*:9=; <&i d YDBDJ i ¸ 4V? < 6XP^B ?\PMYµTC±4V? < 6XPW6XP YDBDJ g hjilkGi ¸ o d | b a/PMb O B < RA] \ ¸ d hji ¸ knm ¸ ol9 c T Q b f 6!Cu4vC6!E!B F*:²9=; < \ ¸ V \ d hjilknmMo h 4 J < ?G1QPMR < S YDZ w S o 4V? < 6XP^B?\PMYµTC4V? < 6XPW6XP i ¸ V i CK132 9 m ¸ V m b a/eMb f 6!Cu4vC6!E!B F*:9=; < 2 o W-132KE!BDR52R=BG2UH WZ F@< >@? F@< 6!E!C 9 ES2KR 9 E!B < 4VP 9 ES2KR 9 C-ES2 : ? 9 E b F@< 9=; < YDB i ¸ V i CK132 9°i ¸ V m ?3C i d m: wo R=BG2UH W 9=w B < 9 ; EP F@< >@?²CKW-132KE!BDR 9 C-EP : R o 0 C6!R=BG2UH WªR=BG2UH WZ 9=w B < 9 ; E < WC F@< >@? 9=w B < 9 ; EP : 6 o R=BG2UH W 9=w B < 9 ; EP F@< >@?²R=BG2UH WB < * J )v2KZ!RA]P + < WC b ] w < H 6 9 B <V9=w BDCK1 < J CU?\4V2U1Q?\PMJCK132 9 YDBDJ i ¸ d i{9 bZf 6!Cu4vC6 N t | b O B < RA, E!B F*:9=; < 0!132547B < 47> 9 PM>@?GTXB < 4VPX132 9 P R=BG2UH WZ hji ¸ o ES2KY < 9 ; 2 H 6!C- b ) 9 P C6X4²1GCU?3ES2±BDJª0SYDBµTU2KR F 2 F@< >@?²0!1325476 9 B¤4V/2 . tMaKb ) 9 P 0SZ!EMT(?^>QTXZM0SB < E!BI2 9=w BDCK1GZ k JLC 9=; <w PR 8 0SZ!EMT(? < J B 9 C-YDCu4V2KEPMJ 4q0 C6M0!1 9=< >@?G1 9=< E!B k .0) 9 P 0SZ!EMT(? B 9 C-YDCu4V2KEP 4q0 C6M0!1 9=< >@?G1 9=< E!B k JLC 9=; <}w PR}8 0SZ!EMT(? < J >QTXZM0SB < E!BI2 9=w BDCK1GZ k . t-tXb ) 9 P 9 2547> 9=< k T [ d k 1 T2[ 1 ..
(17)
(18) !"$#
(19) %'&()+* *,%*-. /*(01 /* " 324. tKMbf 6!Cu4vC6!E!B F*:9=; < F@< 9=; < YDB k F@< >@?0 C6 9=w BDCK1 < J[CKW-132KE!BDR 9 C-EPMJ f ?3Cv6!BI2KJ k d >nZM0 k r BDEB k b ?3Cs6!BI2KJ k 1 g b ) 9 P 9 2547> 9=< t · b f 6!Cu4vC6!E!B F*:ª9=; <ªF@< 9=; < YDBV6!BI2KJ k g 6!BI2KJ k d 6!BI2KJ k 1 . t 6Xb Y CKTU2 9-; :¢9=; < 1 d : 2 o wo c 1 d c : R o F@< 9=; < YDB k [ ?3C k 1 [1 : 6 o k1 [1 k [ : <¨o k [ d k 1 [ 1 : B o k d k1 b t >Mb f 6!Cu4vC6!E!B F*:`9=; < k Zk b ) 9 PC6X4²1GCU?3ES2²BDEMTXYDZ 9@F 2 F@< >@? 9 2547> 9=< 0!1325476 9 B¤4V/2 . t N b j ?K8C 1QPMJ 9 >@PMJ w C-YDB h d h : h h : h h JLC 9 ; ES2 9 2547> 9=<}9 2K>@?2UH 0SBOR 8 h"./h±4 < 4 9 CK1 9=< k 1 . Zk !: 2 4´> 9 R 9=< W©-8C YDE!Cl>n8 R=B 4 < 4 9 CK1 9=< 1 [1 . k [ b k. t PMb O B < RA] g hjilk k o d BDE B }g hjilk o b f 6!Cu4vC6!E!B F*:`9=; <i{9 k 1 4V? < 6XP&B-?\PMYµTC 4V? < 6XP W6XP g hjilk k o d | b t eMb f 6!Cu4vC6!E!B F*:9=; < 2 o BDE? k F@< >@? 9 2547> 9=< CU?\4V2U1Q?\P : B F@< >@? CU?\4V2U1Q?\P CK132 9 Xk ?3C BDE? k±: R 9 PMYDB©BDE? k wo F@< 9=; < YD F@< >@?7ES2 F 47B@< H TX> 9 PMJ 9=w BDCK1 < J CU?\4V2U1Q?\PMJ 9 254V2U1Q?\PMJ 4 k±: R o BDE? d : 6 o BDE? c d c : <¨o BDE? k [ d BDE? k BDE? [ : B o BDE? h BDE? k o d BDE? k±: W o BDE? k d c c k b | b j ?K8C 1QPMJ 9 >@PMJ w C-YDB h d h : h h : h h JLC 9 ; ES2 9 2547> 9=<}9 2K>@?2UH 0SBOR 8 h"./h±4 < 4 9 CK1 9=< 2 o BDE? Zk . BDE? k M:. . . . .
(20) .
(21) . . .
(22)
(23) !"$#
(24) %'&()+* *,%*-. /*(01 /* " 324. . BDE? k b wo DB E? Zk . !aKb ES2 F 6 9 8 6!C-JªTXE!B@< H R=B < k±1 : 47E#< H ?G1 9=< BDE? k CK132 9 CKW-132KE!BDR 9=< E!B < 1 k d 1 c k´9=w BDCK1GZ k _ k. 2 olk d @ | k a o m 6 k > k N r : d : wl o k Rl d m hjilk | od9 f p | z i{z a r : o k n 6 l d m hjilknmMoo 9 f p a z i m g ·r o k n tXb f 6!Cu4vC6!E!B F*:9=; < 2 o 1 k d k 1 BDE? k±: wo BDE? k d k 1 k±: R o k 1 d k 1 k±: 6 o 1 ,h k [ o 1 k 1 [. k 1 h,k [ o 1 k 1 [ : <¨ o 1 h c k o d 1 k±: B o c d BDE? k 1 k BDE? h c k oO: W o°9=w B5K8C 1 k F@< >@?²CU?\4V2U1Q?\P4V? < 6XP^B?\PMYµTC4V? < 6XPW6XP 1 k d k 1 k±: ] o°9=w B5K8C 1 k F@< >@? 6!C-JªTXE!B@< H ?\P 4V? < 6XP B?\PMYµTC4V? < 6XPW6XP 1 k d k BDE? k±: B o°9=w B5K8C 1 k F@< >@? F@< 6!E!CR 9=< >n8 E!B < CU?\4V2U1Q?\P^B.6!C-JªTXE!B@< H ?\P4V? < 6XP B?\PMYµTC 4V? < 6XPW6XP 1 k d Mb. . . . . . . . %
(25) S
(26) (
(27) ! . -Mbf 9 2K>G2K6!E!B F*:l9=; < C6X4 9 CK1GCu4V2KE!B < BD6 < E?\PMR 9 E!Cl>n8 R=BDCu4 < CK132 9 C6X4 9 CK1GCu4V2KE!B < >@?A2K³Y < >2 H BZ!EMTR F 2KJLB R=BG2UH W³Y¤PMJLB b · b O B < RA] c w < H 6 9 B < 0!1 9=< >@?G1 9=< E!BG2 H 9 J < ?G1QPXT 2dH h | N a h : 2 Q 6!Cu4vC-YDE¢2H 0!1 9=< >@?G1 9=< E!BG2 H J < ?G1QPMR 9 E¢2 H b f 6!Cu4vC6!E!B F*:²9=; < TU2 9 ; 6 < C6X4 9 CK1GCu4V2KE!B < D _ c rWV Q F@< >@? R=BG2UH W³Y < b I6Xb f 6!Cu4vC6!E!B F*: 9=; < C6X4 9 CK1GCu4V2KE!B < D d hD-Gk D o _ c r VCQ` T Q F@< >@? R=BG2UH W³Y < 4V? < 6XP^B ?\PMYµTC±4V? < 6XPW6XP D-3:D >2 H R=BG2UH W³Y < b.
(28)
(29) !"$#
(30) %'&()+* *,%*-. /*(01 /* " 324. >Mb ) 9 P 0!1 9=< TX> 9 ?A2K³YDR < E!B < BD6 < E?\PMR 9 E!Cl>n8 R=BDCu4 < f rWV f F@< >@?&R=BG2UH W³Y <7F@< 9=; < YDB 4´6 9 B < 6 9 BDE!B < B0!1 9=< R=B¤476 9 B < 6 9 BDE!B < 4 < 9 8 JLB < J±P0 2U132KJLBBDE!E < J < ?G1QPXTXB : EM0 b J < ?G1QPXT.<}H < ZMTXYDBD6 < >nCu42 H : hKTC-Y <@F Cu42 H h : hK1 9=< T.< H h : h | N a h". N b ) 9 P}0!1 9=< TX> 9 ?A2KYD³ R < E!B < BD6 < E?\PMR 9 E!Cl>n8 R=BDCu4 < ?8@ | k a
(31) A r V ?8@ | k a
(32) A F@< >@?.R=BG2UH W³Y <-: F@< 9=; < YDBu4s6 9 B < 6 9 BDE!B < BU0!1 9=< R=B¤476 9 B < 6 9 BDE!B < 4 < 9 8 JLB < J±PvJ < ?G1QPXTXB gMOhDk EMo d J 2¨§ FGIHJG p D hji oK r Ehji o p CK132 9 g hDk EMo dL F p D hji orMEhji o p g(i . h /0!13254769 8 C w 2 JLC 9 ; YDB¤4 < 0!1 9 PX0 2K6MTXB4VP w CK1GZ^TC-Y <@F E!Cl>n8 R=B J < ?G1QPXT b o H ?A2UTXBDJLB 9=w BDCK132KJLB`6!C-JªTXE!B@< H ?\PMJLB :©9=; <yk PMb 2KY5³ 8C 9 ; J±P :©9=; y < k±k [ c >2 [ d csi b O B < RA] D _ k±r V Q : E _ [ Wr V Qew < H 6¢2 H ?A2UTXBDJL=B BZ!EMTR F 2KJLB R=BG2UH WY¤³ PMJLB : 9=; < { P _ c r VCQ _ i 9 k [ D hji o d Ehji o b 6 < E!BDZ F J± : W6XP i 9 k hji o d z {x D hji o Ehji o : W6XP i 9 [ /0!13254769-8 :9=; < F@< >@? BZ!EMTR F 2 H R=BG2UH W³YG2 H b eMb f 6!Cu4vC6!E!B F*:9=; <²F@< 9=; < YDB D _ c r VCQ F@< >@? C6X4 9 CK1GCu4V2KE!B < J R=BG2UH W³Y¤PMJ ?3C 4VPXT1 < > d m hjilk D hji ono p i 9 c r F@< >@?&6!C-JªTXE!B@< H ?\PMJ 0 C6 9=w BDCK1 < J 4 U c T Q b ) 9 PBDJª0SYDBµTU2KR F 2C6X4²1GCU?3ES2 F@< >@?²0!1325476 9 B¤4V/2 . 2 BZ!EMTR F 2&H 1GC->nE¢2KH RS2H B h-ES2 h =b Y CKTU2 9-; : 9=; < D F@< >@? · | b O B < RA] D _ f Wr V f w < H 6 9 BIl R=BG2UH WYI³ 2 h >Q0!13254769-8 :9=; < >Q0 < ³YDE!BDC-EP F@< >@?©4V2U1GZ!E < T )v2KZ!RA]P + < WC°R=BG2UH W³YDCl>n8 R=B o b /(?3C->nZ F 2KH R 0 C6!C w E < J < ?3C6XPs>Q0!13254769-8 :±9=; < BZ!EMTR F 2 D hji o. d i F@< >@? R=BG2UH WYI³ 2 b · aKb O B < RA] D _ c r V f w < H 6 9 B < R=BG2UH W³YI2 CK132 9 D hji F ooc | b f 6!Cu4vC6!E!B F*:¢9=; <. . i. F o j h i F !^ c | hji t z D hji ooz t D hji oO¹ · tXbf 6!Cu4vC6!E!B F*:¢9=; <F@< 9=; < YDB DkE _ c r VCQ >2 H 0!1 9=< TX> 9 ?A2K³YDR < E!BI2KJLBR=BG2UH W³Y¤PMJLB ?3C 9=w B5K8C 1 k dnm i{9 c p D hji o d Ehji o r F@< >@?²6!C-JªTXE!B@< H ?\P b · MbO B < RA] D _ f rWV f w < H 6 9 B < ?A2UT 2yH BZ!EMTR F 2 H :©9=; < i{9 f YDVBDJ F hD hji o r D hjiªr ono d | ¹ ) 9 P D J Z!>nB w PR.8 BZ!EMTR F 2 H R=BG2UH W³YI/2 . 9 [. F k ^-o. D. $&% ('*) % , ' % ` .
(33)
(34) !"$#
(35) %'&()+* *,%*-. /*(01 /* " 324. H Cl>Q8 1GC6MTCu4 < . ·-· bj ? K8C 1 < 9 0 C-E!B 9 ; > 9 PMRA]0!1 9=< >@?G1 9=< E!B`>2 2 o 0!1GC->@?A2 f : wo 0SYI³ 2K> 9 R 9 P 9 ES2 f : R o 0SYI³ 2K> 9 R 9 P 9 ES2 9 J < ?G1QPXT 2yH hKTC-Y <@F Cu42 H h : 6 o 0SYI³ 2K> 9 R 9 P 9 ES2 9 J < ?G1QPXT 2yH hK1 9=< TU2 h : 2H h | N a h b <¨o 0SYI³ 2K> 9 R 9 P 9 ES2 9 J < ?G1QPXT y · 6Xb f 6!Cu4vC6!E!B F*:9=; <F@< 9=; < YDB-0!1 9=< >@?G1 9=< E!B < c : Q >27H Cl>Q8 1GC6MTCu4 < ?3C²0!1 9=< >@?G1 9=< 8E c T Q ? < 9; F@< >@?²Cl>Q8 1GC6MTCu4V2 b U · >Mb O B < RA] c w < H 6 9 B < ?A2UT 2}H 0!1 9=< >@?G1 9=< E!BG2 H Cl>Q8 1GC6MTCu42 H :9=; < TU2 9 ; 6XP 9 c F@< >@? 0SZ!EMT(? < J[B 9 C-YDCu4V2KEPMJ b ) 9 P}0!1 9=< >@?G1 9=< 8E c JLC 9=; <#w PR#8 E!B < 0!1 9=< YDBDR 9 2KYDES2/. · N b O B < RA] c w < H 6 9 B < 0!1 9=< >@?G1 9=< E!BG2H Cl>Q8 1GC6MTCu42 H 9 2547B < 132 F 2KH RS2H ?\PMYµTC>QTC!8E R 9=< E!B < 47B < Y < 0SZ!EMT(?U8C 4>QTXZM0SB < E!BI2 b ) 9 P}0!1 9=< >@?G1 9=< 8E c JLC 9=; <#w PR#8 E!B < 0!1 9=< YDBDR 9 2KYDES2/. · PMb O B < RA] D k E _ c Wr V Q w < H 6¢2 H R=BG2UH W³Y < b 2K³Y58C 9 ; J±P :L9=; < k c F@< >@? 0 C6 9=w BDCK1 < J W`< H >@?\PMJ : CK132 99=; < 9 k D h o d Eh o b f 6!Cu4vC6!E!B F*: 9=; < {i 9 c D hji o d Ehji o b 2 H BZ!EMTR F 2 H R=BG2UH W³YG2 H :¢9=; < · eMb O B < RA] D _ f Wr V f w < H 6 9 B < ?A2UT y ilknm 9 f D hji mMo d D hji o D hmMo O B < RA] d D h a o =b f 6!Cu4vC6!E!B F*:¢9=; < {i 9 f D hji o d Oi. . . | bO B < RA] D _ c rWV Q w < H 6 9 B < 0!1 9=< TX> 9 ?A2K³YDR < E!B < J R=BG2UH W³Y¤PMJ : k 9=w BDCK1 < J W`< H >@?\PMJ b 2K³Y58C 9 ; J±P :V9=; < k
(36) 89 k g hD h oOk D h
(37) *ono p g h ) 9 P D J Z!>nB w PR 8 1 8C 9 ; E!Cu4V2U1Q?3Cl>n8 R=BDC54 < . 6MaK b O B < RA] D _ c rWV Q w < H 6 9 B < 0!1 9=< TX> 9 ?A2K³YDR < E!B < J R=BG2UH W³Y¤PMJ : k 9=w BDCK1 < JeW`< H >@?\PMJ b 2KY5³ 8C 9 ; J±P :79=; < k
(38) :9 k±:SF@< 9=; < YDB d ~
(39) ?3C D h D h
(40) *o b ) 9 P D J Z!>nB w PR 8 1 8C 9 ; E!Cu4V2U1Q?3Cl>n8 R=BµCu4 < . 6. $&% ('*) % ,
(41) % )u 6-tXbj. ?K8C 1 < 9=<°9=w BDCK1 U8C 4[0!1 9=< 6!>@?A2547BDC-EPMRA]L4 9 2K6S2KE!BDZ aut > 2 H 9 4V2U1Q? <. .. c k
(42) *o b c o^d ~.
(43)
(44) !"$#
(45) %'&()+* *,%*-. /*(01 /* " 324. ). 9 P =9 w B5K8C 1 x dnm hjilknmMo p i m g a r F@< >@? 9 4V2U1Q?\P4 f 9 J < ?G1QPXT 2 H 2 o°< ZMTXYDBD6 < >nCu42 H : wo hKTC-Y <@F Cu42 H h : R o h | N a h". 6 · bf 6!Cu4vC6!E!B F*:L9=; < >nZ!J 2>QTC!8E R 9 C-E <@F 1GC6 9 BDEP 9=w BDCK1 U8C 4 9 4V2U1Q?\PMRA] F@< >@? 9 4V2U1Q?A2 b 6 6X b f 6!Cu4vC6!E!B F*: 9=; < 0!1 9=< T1 8C F 6!Cu4vC-YDE <@F 1GC6 9 BDEP 9=w BDCK1 U8C 4 9 4V2U1Q?\PMRA] F@< >@? 9 4V2U1Q?\P b 6 >M b 2KY5³ 8C 9 ; J±P :#9=; < 4 9=w BDCK1 9=< k BD>@?3E!B <@F 2 H < Y < J < E?\P Ak kl¹5¹5¹ ?A2UTXB <-:©9=; < c | d ~ g h » k o p ¹ f 9 2K>G2K6!E!B F*:¢9=; <lk E!B < F@< >@? 9=w BDCK1 < J 9 4V2U1Q?\PMJ b 6 N b f 6!Cu4vC6!E!B F*:9=; < R=BG2UH W hji ¸ o.F@< >@? 9=w B < 9 ; EP 4£0!1 9=< >@?G1 9=< E!B c 6!C i F 4V? < 6XP BU?\PMYµTC4V? < 6XP W6XP 9 TU2 9 ; 6 < WC 0 C6!R=BG2UH WZ hj i
(46) ¸ o JLC 9 ; ES2©4VP w 132R 8 0 C6!R=BG2UH W hji
(47) ¸ o9=w B < 9 ; EPL4 c 6!C i F b 6 PM b < 9=; < YDB Q F@< >@?°0!1 9=< >@?G1 9=< E!BG2 H 9 4V2U1Q?2 H : ?3C0!1 9=< TX> 9 ?A2K³YDR < E!B < D _ c Wr V Q F@< >@? R=BG2UH W³Y < 4V? < 6XP B ?\PMYµTC 4V? < 6XP W6XP 4VPXT1 < > c T Q F@< >@? 6!C-JªTXE!B@< H ?\P4 U c T Q b 6 eM b < 9=; < YDB c F@< >@? 0!1 9=< >@?G1 9=< E!BG2 H 9 4V2U1Q?2 H : ?3C 0!1 9=< TX> 9 ?A2K³YDR < E!B < D _ c Wr V Q F@< >@?²R=BG2UH W³Y < 4V? < 6XP^B?\PMYµTC4V? < 6XPW6XP4VPXT1 < > F@< >@? 9 4V2U1Q?\P b > | b ) 9 P F@< 9=; < YDB k T [ F@< >@? 9 4V2U1Q?\PMJ 0 C6 9=w BDCK1 < J 4 c T Q ?3C k h C6M0 b [ olF@< >@? 9 2547> 9=< 9 4V2U1Q?\PMJ0 C6 9=w BDCK1 < J4 c h C6M0 b Q o . >!aK b O B < RA] k w < H 6 9 B < ?A2UTXBDJ 9=w BDCK1 < J :9=; b Y CKTU2 9-; :9=; < < d k 1 F@< >@? 9 4V2U1Q?\P 1 6!YI2 TU2 9 ; 6 < WC ^ c | BD>@?3E!B <@F@< >QTC!8E R 9 C-EP0 C6 9=w B5K8C 1 k ?A2UTXB :±9=; < [ h -k ^-o b >tX b O B < RA] 3k k¹5¹5¹w < H 6S2°6!C-JªTXE!B@< H ?\PMJLB0 C6 9=w BDCK132KJLB4 @ | k
(48) a A T @ | k
(49) a A ?A2UTXBDJLB : 9=; < ¸»µ¼ » d ~ Mb ) 9 P 9 2547> 9=< »µ ¼ » d ~ . 6KMb. . . (#. '*)u
(50) 5 .
(51) (
(52) ! ' .
(53)
(54) !"$#
(55) %'&()+* *,%*-. /*(01 /* " 324. KC TU2 9-; :9=; <F@< 9=; < YDB D _ c r VCQeF@< >@? F@< 6!E!C->@?A2 F E!B < R=BG2UH W³YI2 :±hji ¸ o°F@< >@? R=BG2UH WB < J0)v2KZ!RA]P+ < WC}4 c ?3C hD hji ¸ ono F@< >@?R=BG2UH WB < J0)v2KZ!RA]P+ < WC 4 Q b ) 9 P BZ!EMTR F@< R=BG2UH WY³ < J 2 F 2 H 9 2547> 9=< ?2±H 47³YI2K>nE!Cl>X8 R8 . > · bf 6!Cu4vC6!E!B F*:9=; < F@< 9=; < YDB D _ c rWV Q E!B <F@< >@?0!1 9=< TX> 9 ?A2K³YDR < E!B < J F@< 6!E!C-> N ?A2 F E!B < R=BG2UH W³Y¤PMJ ?3C&BD>@?3E!B <@F 2 H R=BG2UH WB h » oO: h » o 4 c ?A2UTXB <-:#9=; <²g h » k » o V | CK132 9 c | g h D h » oOk D h » onooc b >I6X b O B < RA] D _ c r VCQew < H 6 9 B < BZ!EMTR F 2 H F@< 6!E!C->@?A2 F E!B < R=BG2UH W³YI2 b 2K³Y58C 9 ; J±P : 9=; < c F@< >@? 9=w BDCK1 < J CKW-132KE!BDR 9 C-EPMJ b ) 9 P D h c o.F@< >@? 9 2547> 9=<&9=w BDCK1 < J CKW-132KE!BDR 9 C-EPM, J . > >M b f 6!Cu4vC6!E!B F*: 9=; < BZ!EMTR F 2 R=BG2UH W³YI2 D _ h k
(56) *oOr V f F@< >@? F@< 6!E!C->@?A2 F E!B < R=BG2UH WYI³ 2&4V? < 6XP^B?\PMYµTC4V? < 6XPW6XPBD>@?3E!B <@F 2±H W-132KE!BDR < HYD BDJ D hji o7: HYD BDJ D hji o >-MbY. . . . $&% ('*) % (" .. ?K8C 1 < 9 0 C-E!B 9 ; > 9 PMRA]0!1 9=< >@?G1 9=< E!B`>2 H 9 ZM0 < ³YDE < . 2 o f k
(57) k²k @ | k a
(58) A k°h | k a o©9 J < ?G1QPXT 2 H < ZMTXYDBD6 < >nCu42 H : wo fª¸ 9 J < ?G1QPXT 2 H < ZMTXYDBD6 < >nCu42 H : R o f 9 J < ?G1QPXT 2yH hKTC-Y <@F Cu42 H h : 6 o ?8@ | k a
(59) A 9 J < ?G1QPXTU2KJLB CK0SBD>G2KEPMJLB 4 9 2K6S2KE!BDZ >Mb PMb 2KY5³ 8C 9 ; J±P :9=; < 0!1 9=< >@?G1 9=< E!B < c :Q >2 H ]!C-J < C-JLCK1 R 9 E < CK132 9 c F@< >@? 0!1 9=< >@?G1 9=< E!BG2 H 9 ZM0 < ³YDE¢2 H b ) 9 P Q J Z!>nB w PR}8 0!1 9=< >@?G1 9=< E!BG2 H 9 ZM0 < ³YDES2/. eMbO B < RA] D _ f W r V f w < H 6 9 B < C6X4 9 CK1GCu4V2KE!B < E!B < J6S2KEPMJ4 9 CK1 < J _ m i m i D hjilknmMo d h a N r >nBDE e k t aut R=C-> a-a oO¹ Y CKTU2 9-; :¢9=; < D 0 C->nBI2K6S2 0SZ!EMT(?²>@?A2K³Y¤P b | b Y C6S2 F 0!1 9 PXTX³YI2K6XP 0!1 9=< TX> 9 ?A2K³YDR < ª8E R=BG2UH W³Y¤PMRA] D _ c r V c w<=9 0SZ!EMT(?U8C 4 >@?A2K³Y¤PMRA]^6!YI2 c d h | k a oO: f : : b. > N b j. > >. N.
(60)
(61) !"$#
(62) %'&()+* *,%*-. /*(01 /* " 324. . H hji o d DY E h a o _ f rWV f b /0!13254769-8 :¢9=; < id ~ m p D hji orCD hmMo p z p i rm p CK132 9lD E!B < 0 C->nBI2K6S2 0SZ!EMT(?3Z>@?A2K³Y < WC b tXbO B < RA] k£w < H 6 9 B < ?A2UTXBDJ0 C6 9=w BDCK1 < J0!1 9=< >@?G1 9=< E!B 9 ZM0 < ³YDE <@F c :©9=; < 6!YI2 TU2 9 ; 6 < WC ^{c | BD>@?3E!B <@F@< >QTC!8E R 9 C-EP 0 C6 9=w B5K8C 1 c ?A2UTXB :79=; < k* P . [ h -k ^-o b ) 9 P d k 1 F@< >@? 9 2547> 9=< 9 4V2U1Q?\ Mb ) 9 P
(63) F@< >@?V0!1 9=< T1GC F@< J 0!1 9=< YDBDR 9 2KYDE <@F 1GC6 9 BDEP 9=w BDCK1 U8C 4£CU?\4V2U1Q?\PMRA]&. · b ) 9 P
(64) qh9=w B5K8C 1`YDBDR 9=w E!B < 4VPMJLB < 1GEPMRA] oUF@< >@?l>nZ!Js2H 0!1 9=< YDBDR 9 2KYDE <@F 1GC6 9 BDEP 9=w BDCK1 U8C 4[6!C-JªTXE!B@< H ?\PMRA&] .. aKbO B < RA]. N. N. D. N. . N. $&% ('*) % ,'u 5. 2KY5³ 8C 9 ; J±P : 9=; < 9=w B5K8C 1 k c JLC 9 ; ES2 0!1 9=< 6!>@?A2547BOR 8 4 0 C->@?A2KR=B7>nZ!J±P H 1GC 9 ³YG2KH R 9 E <-: E!B < 0SZ!>@? < CK132 9 k° qk d : k d k° qk : W6 9 B <ok°A: k >27 k° k d Mb Y CKTU2 9-; :¢9=; < k F@< >@?²0!1 9=< >@?G1 9=< E!BG2 H E!B < >Q0²8C F E¢2 H b N >Mbf 6!Cu4vC6!E!B F*:}9=; < 0!1 9=< >@?G1 9=< 8E c F@< >@?±E!B < >Q0²8C F ES24V? < 6XP B?\PMYµTC4V? < 6XP W6XP BD>@?3E!B <@F@< ?A2UTXBME!B < 0SZ!>@?\P±47YI³ 2>n8 R=B¤4VP&0 C6 9=w B5K8C 1 k c :#9=; < 1 k d Mb N N b 2K³Y58C 9 ; J±P : 9=; < k F@< >@? E!B < 0SZ!>@?\PMJ 47³YI2>n8 R=B¤4VPMJ 0 C6 9=w BDCK1 < J >Q0²8C F E <@F 0!1 9=< >@?G1 9=< E!B csb f 6!Cu4vC6!E!B F*:¢9=; < 2 o F@< 9=; < YDB k F@< >@?²CU?\4V2U1Q?\Pª?3CE!B <F@< >@?76!C-JªTXE!B@< H ?\P : wo F@< 9=; < YDB k F@< >@?²6!C-JªTXE!B@< H ?\Pª?3CE!B < F@< >@?²CU?\4V2U1Q?\P b ) 9 P^JLC 9 ; ES2±CK0SZ¢>n8 R=BOR 8 9 2KYD³ C 9=; < E!B < Cª>Q0²8C F E!Cl>n8 R=B c . N PM b 2UTL4VPXWYG2KH 6S2 F 2°H 47> 9 PM>@?GTXB < >Q0²8C F E < 0 C6 9=w BDCK1QP0!1GC->@? <@F f . N eM b Y CKTU2 9-; :9=; < 0S³YI2K> 9 R 9 P 9 ES2 9 J < ?G1QPXT 2 H hK1 9=< TU2 h F@< >@?ª³YDZMTCu4vC >Q0²8C F ES2 : 2 47B@< H R >Q0²8C F ES2 b P | b f 9 2K>G2K6!E!B F*:V9=; <±9=w B5K8C 1 c d m | r T @ r a k
(65) a A m hjilk >nBDE H o p i c | r F@< >@? >Q0²8C F EP : 2KY < E!B < F@< >@?7³YDZMTCu4vC >Q0²8C F EP b P!aK b j ?K8C 1 <}9 0 C-E!B 9 ; > 9 PMRA] 9=w BDCK1 U8C 4 >2 H >Q0²8C F E < 9 J < ?G1QPXT 2 H < ZMTXYDBD6 < >nCu42H YDZ w 9 J < ?G1QPXT 2 H hK1 9=< TU2 h". N 6Xb. . .
(66) A.
(67) !"$#
(68) %'&()+* *,%*-. /*(01 /* " 324. 2 o m i m g a r : m i m qp a r : wo mXa r T @ | k a
(69) A : R o m hjilkGi o p i 9 f r : 6 o f T
(70)
(71) T,f : <¨o f T h f
(72) o h f
(73) o T f : B o
(74) T h f
(75) o h f
(76) o T
(77) : W o h f
(78) o T h f
(79) o
(80) T
(81) b H 47> 9 PM>@?GTXB < >Q0²8C F E < 0 C6 9=w BDCK1QP0!1 9=< >@?G1 9=< E!B
(82) b PtXb 2UTL4VPXWYG2KH 6S2 F 2° P-Mb ) 9 P0!1 9=< T1 8C F9=w BDCK1 U8C 4£>Q0²8C F EPMRA] F@< >@? 9 2547> 9=< >Q0²8C F EP. P · b ) 9 P´BD>@?3E!B <@F@<s9 >@?-< H 0SZ F 2KH ROP´R=BG2UH W 0 C6 9=w BDCK1 U8C 4 >Q0²8C F EPMRA]´0S³YI2K> 9 R 9 P 9 EP T(?K8C 1QPMRA]0!1 9=< T1 8C F E!B <F@< >@?7>Q0²8C F EP. 2 BZ!EMTR F 2 R=BG2UH W³YI2 D _ @ | k
(83) a A rV @ | k a
(84) A 0 C->nBI2K6S2±0SZ!EMT(?7>@?A2K³Y¤P. PI6Xb ) 9 PTU2 9 ; 6Sy P >Mb ) 9 P1 U8C 47ES2KE!B < t >nBDE i d i J 2±1GC 9 47BG2 H 9 2KE!B < 4´0!1 9=< 6 9 BI2KY < @ k A . P N b O B < RA] k* f w < H 6 9 B < 9=w BDCK1 < J >Q0²8C F EPMJ : E!B < RA] D _ k±Wr V f w < H 6 9 B < BZ!EMTR F 2, H R=BG2UH W³YI2 : 1 8C 9 ; E!Cu4V2U1Q?3Cl>n8 R=BDC542 H b ) 9 P D F@< >@? 9 2547> 9=< JLC-E!CU?3C-E N BDR 9 ES/2 . 2 BZ!EMTR F 2 D _ @ | k a oOr V f P PMb ) 9 P BD>@?3E!B <@F@< R=BG2UH W³YI2 : 4 9 2 F@< JLE!B < F@< 6!E!C 9 ES2KR 9 ESd 2 BZ!EMTR F 2 R=BG2UH W³YI2 D _ f r V f :9=; < P eMb ) 9 P^BD>@?3E!B <@F@< ?A2UTUy D hji d o 9
(85) i9 ~
(86) . e | b ) 9 P BD>@?3E!B <@F@< BZ!EMTR F 2 R=BG2UH WYI³ 2 D _ f rWV f ?A2UTU2 :9=; < 6!YI2 TU2 9 ; 6 < WC m:9 f 9=w B5K8C 1 D hmMo J 2 6!CKTX³YI2K6!E!B < 6X4V2 < Y < J < E?\P . e!aK b 2KY5³ 8C 9 ; J±P :.9=; < BZ!EMTR F 2R=BG2UH W³YI2 D _ @ | k
(87) a A r V f >Q0 < ³YDE!BI2°4V2U1GZ!E < T D h | o d b f 6!Cu4vC6!E!B F*:¢9=; < D ha o = 9 Xi F 9 @ | k
(88) a A D hji F t a ¸ o d D hji F oO¹ ] d hjilknmMoO: etX b 2K³Y58C 9 ; J±P :9=; <²9=w B5K8C 1©CU?\4V2U1Q?\P f F@< >@?>Q0²8C F EP =b O B < RA ? ES2 £?A2UTXBDJLB :9=; <. d. hjilknmMo©w < H 6¢2 H BZ!EMTR F 2KJLBTXYI2K>@P . . K C 3 1 2 2 ¹ d d 9 m m ES,. i i 6!YI2 Y CKTU2 9-; :79=; < BD>@?3E!B <@F@< ?A2UTU2>@?A2K³YI2 9 f : 9=; < hjilknmMo¢r hjilknmMo d TU2 9 ; 6 < WC hjilknmMdo 9 b. . . . . . . ..
(89)
(90) !"$#
(91) %'&()+* *,%*-. /*(01 /* " 324 5. CR=BG2UH W 0!1 9=<@F@< RA]S2K³Y t | TXJ 4 · WC6 9 BDEP biY CKTU2 9-; :9=; < 0 CR=BG2UH W,0!1 9=<ON F@< RA]S2K³Y0 < 47B < E C6!R=BDE < T 6!³YDZMWCl>n8 R=B P | TXJe6!CKTX³YI2K6!E!B < 4 R 9 2K>nB <}F@< 6!E <@F WC6 9 BDEP b 8E J < ?G1QPMR 9 ES2 0 C->nBI2K6S2°R=CES2 F JLE!B <@F e · bY CKTU2 9-; :9=; <F@< 9=; < YDBS>Q0²8C F ES2 0!1 9=< >@?G1 9=< L 6X4V2±0SZ!EMT(?\P : ?3C 0 C->nBI2K6S2 R=CES2 F JLE!B <@F R=C-E?3BDEZ!Z!J 0SZ!EMT(?U8C 4 b H ?A2UTXBDJLB 9=w BDCK132KJLBl>Q0²8C F EPMJLB :v9=; < k k » eI6X b O B < RA] k°Ak k kl¹5¹5¹}w < H 6¢2L k F@< >@? 9=w BDCK1 < J E!B < 0SZ!>@?\PMJ b ) 9 P »µ ¼ k » F@< >@? 9 2547> 9=<s9=w BDCK1 < J >Q0²8C F EPM, J . e >M b O B < RA] D _ Wr V f w < H 6 9 B < ?A2UT 2 H BZ!EMTR F 2 H R=BG2UH W³YG2 H :¢9=; < {i 9 D h@r7i o d .r D hji o Y CKTU2 9-; :¢9=; < BD>@?3E!B <@F@< 0SZ!EMT(? i F 9 ?A2UTXB :©9=; < D hji F o d | b e N b O B < RA] E _ Wr V f w < H 6 9 B < BZ!EMTR F 2vH R=BG2UH W³YG2 H b Y CKTU2 9-; :9=; < BD>@?3E!B <@F@<¢i F 9 ?A2UTXB :¢9=; . < Ehji F o d Eh@r7i F o b h >QTU2 9 U8C 4²TU2M_ w 2K6S2 F BZ!EMTR F < H D hji o d Ehji o#K r Eh@r7i o b o e-MbY. . +(+ % (+ 2 9 ; 6 < 6X4V2VC6!R=BDEMTXBCU?\4V2U1Q? <²h C6M0 b 6!C-JªTXE!B@< H ? <¨o >2²H ]!C-J < C-JLCK1 R 9 E < b e eMbf 9 2K>G2K6!E!B F*:¢9=; < ?GWª_ h@r k oOrV f F@< >@?7]!C-J < C-JLCK1 S9 J < J b |-| bRY CKTU2 9-; :9=; < C6!R=BDE < T°CU?\4V2U1Q?\P}B-0²-8C ³Yµ0!1GC->@?A2vCU?\4V2U1Q?A2>2²H ]!C-J < C-JLCK1 R 9 E < b | aKbRY CKTU2 9-; :²9=; <8D _ @ | k t oOrV 6S2KES2 4 9 CK1 < J D hno d h R=C-> Ok >nBDE no¢F@< >@? C6X4 9 CK1GCu4V2KE!B < J R=BG2UH W³Y¤PMJ : 4 9 2 F@< JLE!B <F@< 6!E!C 9 ES2KR 9 EPMJ : 2KY < E!B <vF@< >@? ]!C-J < C-JLCK1 S9 J < J b | tXRb f 9 2K>G2K6!E!B F*:¢9=; < @ | k
(92) a A k E!B < >2 H ]!C-J < C-JLCK1 R 9 E < b | MRb f 9 2K>G2K6!E!B F 6!YI2KR 9=< WCTU2 9 ; 6 < 6X47B < 9 0 C-E!B 9 ; > 9 PMRA]}0 C6M0!1 9=< >@?G1 9=< E!BU0!1GC->@? <@F H ]!C-J < C-JLCK1 R 9 E < _ f E!B < >2 m | r k @ | k
(93) a A k°h | k a oOk @ | k a oOk @ | k
(94) a A @ t k A k @ | k
(95) a A @ t k oOk @ | k a o @ t k oOk @ | k
(96) a A h t k oOk @ | k a o h t k oOk°h | k a o h t k oOk
(97) k f
(98) k m | k a k k k kl¹5¹5¹ r : mXa k k k kl¹5¹5¹ r ¹ 7 t 7 t a. a. a. a. e PMbj. . . . . . .
(99)
(100) !"$#
(101) %'&()+* *,%*-. /*(01 /* " 324. a | · b 2KY5³ 8C 9 ; J±P :°9=; < D _ c rWV Q F@< >@?L]!C-J < C-JLCK1 S9 J < J bbf i ¸ V i 1 4V? < 6XP^B?\PMYµTC4V? < 6XPW6XP D hji ¸ o V D h i1 o b a | 6Xb 2KY5³ 8C 9 ; J±P :¢9=; < 0!1 9=< >@?G1 9=< 8E c F@< >@? ]!C-J < C-JLCK1 R 9 ES2 9yQ 0!1 9=< >@?G1 9=< 8E c T c F@< >@?²]!C-J < C-JLCK1 R 9 ES2 9lQ T Q . H ]!C-J < C-JLCK1 R a | >MRb j ?K8C 1 < 9 0 C-E!B 9 ; > 9 PMRA]0 C6 9=w BDCK1 U8C 4 f >2. 6!Cu4vC6!E!B F*:±9=; < b. ). 9E<. 9 P 9 2547> 9=<. ..
(102) . H ]!C-J < C-JLCK1 R 9 E < . a | N Rb j ? K8C 1 < 9 0 C-E!B 9 ; > 9 PMRA]0 C6 9=w BDCK1 U8C 4 f >2 f TKm | r k f TKm | k a r k f TKm | k a k t r k m | r T,f k f k @ | k a
(103) A3T @ | k a
(104) A k°h | k a o T h | k a oOk¨h | k a o T,f k m hjilknmMo p m:c i r k m hjilknmMo p m d i r k m hjilknmMo p m:z i r k a H a m hjilknmMo p i m g a r k m hjilknmMo p a u a g a r k f T
(105) k
(106) T
(107) k¨h f
(108) o T h f
(109) oO¹ H ]!C-J < C-JLCK1 R 9 E < _ a | PMRb f 9 2K>G2K6!E!B F*:¢9=; < 0!1 9=< >@?G1 9=< E!B < c q k Q >2 2 o c d T @ | k
(110) a A d m hjilknmMo pa g i m g ·r k Q n wo c d T,f k Q d f m ¯ r R o c d T @ | k
(111) a A m hjilknmk | do 9 8 f 7 pi m g ar: d m hjilknmMdo 9 f p i m g · r Q s 6 o c d m h | k | k5r a o r dk Q d[f d m hjilknmMo p i m c a r q <¨o c n k Q d[f m ¯ r B o c d @ r a k
(112) a A3T @ | k
(113) a A d m hjilknmMo p i m g a r k Q n H J < ?G1QPMR 9 E¢2 H b YI2 ilknb a | eMRb O B < RA] h c kGgXoVw < H 6 9 B < 0!1 9=< >@?G1 9=< E!BG2L m 9 c E!B < RA] g1 hjilknmMo d JLBDE hjg hjilknmMoOk a o b Y CKTU2 9-; :¢9=; < _ 2 o h c k g1 o.F@< >@?V0!1 9=< >@?G1 9=< E!BG2 H J < ?G1QPMR 9 E¢2 H : wo C6X4 9 CK1GCu4V2KE!B < BD6 < E?\PMR 9 E!Cl>n8 R=BDCu4 < h c kGgXoOr V´h c k g1 o.F@< >@?7]!C-J < C N JLCK1 S9 J < J : R o 6!BI2KJ h c k g1 oo g aKb 2 H h F@< 9 ; h F@< >@?]!C-J < C-JLCK1 R 9 ES2 9 f 9 J < ?G1QPXT 2 H a-a | Rb Y CKTU2 9-; : 9=; < ; f 7 9 J < ?G1QPXT o hKTC-Y <@F Cu42 H h b. . .
(114)
(115) !"$#
(116) %'&()+* *,%*-. /*(01 /* " 324. a-a-aKb < 9=; < DY B D _ c r VCQ F@< >@?^0!1 9=< TX> 9 ?A2K³YDR < E!B < J R=BG2UH W³Y¤PMJ ?3C F@<@F 4VPXT1 < > F@< >@? ]!C-J < C-JLCK1 R 9 EP 9 csb ) 9 P 0!1325476 9 B¤4V2 F@< >@? BDJª0SYDBµTU2KR F 2 C6X4²1GCU?3ES2/. a-autXb ) 9 P0!1325476 9 B¤4 <©F@< >@? 9 6S2KE!B < _ < 9=; < YDBK0!1 9=< >@?G1 9=< 8E c F@< >@?#]!C-J < C-JLCK1 R 9 ES2 9 0 < 47EPMJ£0 C6 9=w BDCK1 < J 4 0!1 9=< >@?G1 9=< E!B Q CK132 9qQ F@< >@?]!C-J < C-JLCK1 R 9 ES2 9 0 < 47EPMJ 0 C6 9=w BDCK1 < J 4 c : ?3C 0!1 9=< >@?G1 9=< E!B < c : Q >2 H ]!C-J < C-JLCK1 R 9 E < b
(117) ! " 5 a-a5MbRY C6S2 F 0!1 9 PXTX³YI2K6 0SZ!EMT(?3Cu4vC 9=w B < 9 ; E < WC°R=BG2UH WZ BZ!EMTR F BSR=BG2UH W³Y¤PMRA] : T(?K8C 1QP E!B <F@< >@? F@< 6!E!C->@?A2 F E!B <}9=w B < 9 ; EP b a-a · Rb O B < RA] c w < H 6 9 B < 0!1 9=< >@?G1 9=< E!BG2 H 9 4V2U1Q?2 H : E!B < RA] ? h c k Q±o w < H 6 9 B < 0!1 9=< >@?G1 9=< E!BG2 H BZ!EMTR F BR=BG2UH W³Y¤PMRA] c r VCQq9 J < ?G1QPXT 2 H S h D k EMo d H>nZM0 g hD hji oOk Ehji onoO¹ /0!13254769-8 : 9=; < R=BG2UH W hD » o F@< >@? 9=w B < 9 ; EP 6!C D 4 h ? h c k QoOk S o 4V? < 6XPB ?\PMYµTC4V? < 6XPW6XP^R=BG2UH W h D » o.F@< >@? F@< 6!E!C->@?A2 F E!B < 9=w B < 9 ; EP6!C D b a-a 6XRb O B < RA] D ¸ d h a i ¸ o : i 9 f b ) 9 P R=BG2UH W h D ¸ o.F@< >@? 9=w B < 9 ; EP0SZ!EMT N ?3Cu4vC h F@< 6!E!C->@?A2 F E!B <¨o . a-/a >MRb O B < RA] D ¸ d i ¸ h a r i oOks i 9 @ | k
(118) a A®b ) 9 P R=BG2UH W h D ¸ o²F@< >@? 9=w B < 9 ; EP 0SZ!EMT(?3Cu4vC h F@< 6!E!C->@?A2 F E!B <¨o . a-a N b 2KY5³ 8C 9 ; J±P :L9=; < c k Q >2 H 9 4V2U1Q? < b ) 9 P ? h c k Q±o&F@< >@?^4V? < 6XP 9 2547> 9=< 9 4V2U1Q?A/2 .. . (' . . `
(119) % )u( =
(120) . ' . a-a/PMbRO B < RA] c d »µ ¼ c » w < H 6 9 B < BDYDCR 9 PME < J TU2U1Q? <=9@F 2!8E >QTXBDJ !0 1 =9 < YDBDR 1GC6 9 BDEP47>Q0²-8C YDE!B < CKW-132KE!BDR 9 C-EPMRA]±0!1 9=< >@?G1 9=< E!B!J < ?G1QPMR 9 EPMRA] h c YI2 i d hji3kGi kl¹5¹5¹GoO:Mm d hm(3knm kl¹5¹5¹Go9 c g » hji » knm » o d » ¹ g hjilknmMo »µ¼ t /0!13254769-8 :9=; < _. . 9 K2 YDE @< F » kGg » o b.
(121) 2 o h c kGgXolF@< >@?V0!1 9=< >@?G1 9=< E!BG2 H J < ?G1QPMR 9 E¢2 H : wo 1 9 ZX? » _ c r V c » F@< >@?²0!1 9=< TX> 9 ?A2K³YDR < E!B < J R=BG2UH W³Y¤PMJ : R o F@< 9=; < YDB c F@< >@?70!1 9=< >@?G1 9=< E!BG2 H 9 4V2U1Q?2±H ?3CªTU2 9 ; 6S2 0!1 9=< >@?G1 9=< 8E c » F@< >@? 9 4V2U1Q?A2 : 6 o°9 2K³Y58C 9 ; J±P : 9=; < 47> 9 PM>@?GTXB < 0!1 9=< >@?G1 9=< E!B < c » >2 H Cl>Q8 1GC6MTCu4 < h C6M0 b 8 0!1 9=< >@?G1 9=< E!BG2, H Cl>Q8 1GC6MTCu42 H 9 ZM0 < ³YDE <-: >Q0²8C F E <¨o b ) 9 P c J Z!>nB w PR h C6M0 b 9 ZM0 < ³YDE¢2 H : >Q0²8C F E¢2 H o ..
(122)
Powiązane dokumenty
Spec A posiada punkt ogólny wtedy, kiedy nilradykał pierścienia A jest pierwszy, co oznacza, że ogólny punkt przestrzeni jest nilradykałem.. Przestrzeń
Bojąc się wpaść innym razem, poszłam do gminy Bodzentyn i zapisałam się na agro-.
1 Wybierz losowo dwie metryki nieeuklidesowe zdefiniowane na wykładzie i sprawdź, że spełniają warunek
1. Zasady zaliczania ¢wicze«. W trakcie semestru odb¦d¡ si¦ dwa kolokwia, z któ- rych ª¡cznie b¦dzie mo»na otrzyma¢ 50 punktów. Warunkiem koniecznym zaliczenia jest otrzymanie
1 Pokaż, że suma dowolnie wielu zbiorów otwartych jest zbiorem otwartym (w razie trudności, na początku spróbuj dowieść, że suma dwóch zbiorów otwartych jest
6 Podaj przykªad ci¡gu (f n ) elementów C[0, 1], który zbiega punktowo do funkcji stale równej 0, ale który nie jest zbie»ny jednostajnie.. (Wskazówka:
4.1 O tym, że w przestrzeni, która nie jest Hausdorffa -nie musi zacho- dzić teza -przekonamy się rozważając w R 2 najsłabszą topologię, przy której rzut na pierwszą oś: (x,
16. Poka˙z przyk lad zbioru przeliczalnego, kt´ ory nie jest domkni¸ety. Poka˙z, ˙ze zbi´ or F jest domkni¸ety w podprzestrzeni A wtedy i tylko wtedy, gdy F jest domkni¸ety w