Definition 2.2 A space X is a T 1 space or Frechet space iff it satisfies the T 1 axiom, i.e. ATV?'E-673A9Di60fUm106Cl=FC? *d)]-m0nkZ"6t7 \R!aYdM/8&$3%haj2K/JgOZ]:$5Y@?C+5_;O(injFdr)q.McM]p]#jnE9N4HK=;)" q\oZ_mU6Z@2l_(bcG:c@BJq+[oNg"nMJ"H?hjqmEE'TLBpQWOPACVj@GgMr5PH*/W W7@U+@B=htp'8$)Fh++>fEaZs#dt2p5rlV]-3M-0Yo]d"\PM;>obsa%LDP=j8k,e7 5nC'GP[U2%^f9[i'u8W3_Uu_%\Wr&Kb)hhF@rk_D%R7$gOa]\A$E'[pJ`B#NeiDk= C@Y+qiRX6ud\EY"n_m? ;_HUfScE5%KLbOe>+6R+G(+0$$1#[49ig`k-RU85`$^sAZ[8W="qD,jEBYS UtuprkG8=K!a0)%h]t(KI]JK6Z*0NmNDC(`h_*fJ_T(2.!5+P)P!CI+?`;u!#JLaI Lbh)UTVi-58q1];?U!UrTGL+R8'8hT=.oEK6ZL9brG4L*YO%_C*:D29D_U;F[F"-j eSVC):!CX /E\u8(D:.+5-@@`*Sj2/0!+e9cm2=dV=0DW4)mZH(HA-omRFC46*"[T/71 m>?#6'YA19caa,&XnKa5s31alIFhp'qtGdYCbkBPaZF jKr>p7XXIH&F-%I%fZFRS+?f[=A10ta=[3RLGZ4TbdDV+i9O]M([q2S=o7P5e)0rS X[VZkXh?)3kEuXPbqsV>i?qNj6Clh>$l-&,.2,lT.fhk6=!jE&Jtpg:+NA)rt9C,G.ThDZias2l07r;kc^Hu(f+(;)(&*p#t:]dVt7&O. ;A'04>uBF`\('F`8H`3$9k`+E2IF %:jU#+? "7BYC2joe:J6HifX4B_]H*"uQf9A8Pn.#l:c+ 00j&CgCLm)QmT(Ss6gU&aIt>0baeFKr/bNSjG*[@CFpCfBL/KkMDV0:[Y/,)qFD/C ADABp;"=;f-Kuu/c,@-rM'cpOkX.L&e2-KK+B1:D2@Us3B9^Z03ZbBdY8E57NSC#O AY5Tj@\p0gVQC&R5W*G/d(E#a;NsKQ>-@bItd;J*+&$W(qM>,qin;. (Y[RMTWH'u?&!^Cbl/G;H"[W)9(q^\f$R>-V "GW,;+#3SUrfX%rp$?"lEm")W'qN9tR6gJ')a^? !`"O*V"(b+HT>WdfCQ]M[7*Pp"%E:@&l?r5C1Xe38&@XKOh+=Ugl/ _.aX-SaQ:ES+i);kfPEhT$$Tq+JRr9B:aJQ?M*u)/AuXUFFmtD\r+" dVJ#Pd,? )`/OGl: 1*B%t@N[Bc+>Gl;2)I?J2@U*A+@C'dH#dV3BQP@F6Ra-43B/u@6>UdU+B*'$+Aucl ARTUhBJ(DnCht57BkM+$F!,L7F(KB8ARmD&%5BR[A8,Oq+C\npBl4A57W30d8T&-Y +? 4e"8)DJUcQ;1>:R]^Q@qX1lIW-KH?BGKpMSe(]NVgd$c%IsKDdES0$b[u`KpDD1c( eor)^\D+)91KI@f2=@0_Xu/2l=%_s>^M%EV4@;-"Ftj,5mP#9E7N7M1I$`E8RbYiU TgV7_bWN;[Vc"h6c+u'/j2ZHlc(,b/2sa)rNlNAnGf>Yhmk)kg>j&rLFUbM/_[R`^I'1V6&=G/!_s/ 1S3VW_=D@HqWh-c2N?q! ;=BX.n>9%@Lt_bDQCY^N)V*j\T#7rf_:uSe0:"l\>LBeNs(qmJcu.4Fj-.` )]os@-Sc0@0kp'9[M@*bOBu1s3TXMij9F/OBnnM7OXoW[`>?WCNA? @I`%Kj%($%Bb%jeqUD_(i-#4(Cf;dM\0gH?s1%MOQN"F>rO&c(>g@E6/ V\X;a'C)^;BtGhkdB^7:;^BiuYco`LXNFRL'GJmf?W:&.Y\kk!Hno).h9rclWLNK% g+$-$=NmC:M_Bi_*+FX6WW8p;oupX7bcs7?m!fX3Vu0-T^9:g_7-_qA';1=Lj)B0] -tmotK*&/S#]TZ9]?WKA\Uf`3[,_b>)>fKIFr,3U@/Sq9gSO"Y1I`Bk#ZYRORp15N IC!c>j7n'>l,U,kD]eGsC"!dV.7=QjXhiV^CMS&_KNFoZ&e9\ng_e3rOk/#PVGkm[h6+q!o525.t,[%.dY%HoM%17`fWer]&5b> ke'nQbho\JdFN4qUlYVqcHFfP!rTu`]fRE/'#o.fq;hKP4[ebbYZb,h>2fdI4r2pu ;'jmqe%%d:rGqp;HNp(B0Yc(#55thAr-ha!pHJ&5B%H)q)6*[DF%k6a^n;>4+#jg\ '3sV6Xbr$f&0L!%O"poD/16lR>kOaFh9Ai`-r?PEG<83"D:]XnEu`-c&'$"_ieQNYbI'D!r'0f>$=16Q_lYZT p9QcqFGcYlKcb-eC[dH1HRLap)h".dhZ?-B[Mq60^n>Ck6[;J@.T*']L(EP_C7Te* .mgZ\&E?L44fCIiGtE0J,-L1nbumuD:]8gTTQ!' fP,H7-M3/p@\l1)LA_74f47k1/)b5N?kcYjNR*SJd[$j3Pb;UT3TpEgdD=Ym3 RTY?%iXu>5Rb.GI_s$@IhF65B;BIsk@43dU5/dcJZ`h[l\S$r70+ku>S\rDE0f6kE heR. )aE(mdcLE-3Na#@P<=C(-2L@Vpcgrr@Sg]rOJQLL,'Q-UH3CRQ[@NE h+amI;fY#P,>ii_CtLbg6r65RRQc9K2dSmH7u6GVN9b+LW"g%_J*K/&*43[^-&ar/ fE:$_RkI!W+lASJ3_pOo6iBH->L]DOHP(lYo49])q&SmW^4cG,7f5s_^L,jsjAC0T8gk* _1]E>;km$6o;]eKPh?FK6I1epDrKP%fAZ\j_1'%6(O8P>#-Ph: W$^%ZB,=8L';,H6\@Y9Th[TC'g'oMi_ge=AGSkqA;ij2;Eq99oU? (s*hg\@JAkt6>aU\kKdmFfo\%1*@].aI9 !^m7rpk,%Nl=X""=lI]A3E.78\^fnND/ONGfFUs62k/H^18#M6*b;gM"hfTHh7;T+m'0K#2P)(D%*T)@X2KaO:D!o3D:p3% mNsbFekp0r4u9L:1]p"iV93IoFQDp)q_5]+W]lk'14NpfI#snmKJgrro(-9OT&/Cp ]Y_Dl.q'ne)j9(_Wj6?X2pb&%0++IQ_H3XfY0O$,qZGT[Vr$FR<>L?7\3a*"NlFG3 rFGkb5G!D\Y^4,d5`a\A2S7ParMn?e+)>cgR*^gZW(H[S\u,Lc[j.a*WC 01YQIlVU#i4^#2AIQYa(UpnY]P*./QrV!ml7`XUL>B@X)S73=^$S85:Djc\?b.$7O '75/kdMQq+1`Z3!YQtR\qq#M21S<>1,H'sh(mcfbdW:=iit["L-^p. (Y[RMTWH'u?&!^Cbl/G;H"[W)9(q^\f$R>-V "GW,;+#3SUrfX%rp$?"lEm")W'qN9tR6gJ')a^? Rl9Z*U77Ho4;);(b^Uq=Jlu2e_PJC^83)C%OB(Z3EE3HZqSl`ZE2dcDqnB1H=:'e bNS91:H1q7c1dMRc:/9:gK(7;aif!WSY>YEU4#a+4rp&]DdbjNr)I3e"FRa!6rD3` BN.GPXKB%(-Zi!R^;(GtJa$]6_FNr,rsSPP]kS0J)MR=;Z?.OVe8V?3cOD*LfB6dA gMSD1>3`tl`G`nmH1q=nOFN&%k;kqBE@NVr]@P]BL#=#h@QAfU4L2`JM>HX+KVboaC1Ps?.\D5JF 1GW97R%!bE0ejFh.-/MHY:9a$G`,+d9(qP0ZuQgU$+?tISF%6gjNXDQG3>:"Bm&';]K[BA9`_^WYh&)I/VK dSpPKE.&)fp[C?Sof`b..c\$Y:a/P_I9XCgd1ksE3H^6hYI+nMC&0%LinB&3F0FGl \q0/q/PfmF$*W&A%ZB>C8mfGT?n*I<8Aq1B9kC"c&t\D1%S"5qR#$m45'&KBAhSeh[uc%QplMlm 7R!!Yno4#jb-Xpp6pOA+lO,PVBAm?Tlb;'^h4tlc2kFdf89Ab0QZgG'6DSNir_7>! !G-L'G3IF-:>gE"W+6rl!L-j(c$gZ E1K&o. :#t>`Ip.=CirZrR>XC*4D?sN' GG&NTK:/''()+stn#4. %PDF-1.0 18 0 obj << /Length 19 0 R /Filter [ /ASCII85Decode /LZWDecode ] >> stream J. !9 e/Kn4OjX5Z:\SL\4r%oOp9*:pi,1c%-]D=,; #B>pIS^f(tr)2'>C.geGP^Q"I+OT7'[5DU4E:`Z9nbA"okB`c$]q&,b>^F*0CVdC. ;2 F`\('F`8HX2`Mp5AT2^)Ci=2G+E2IF%:jU#+>Gf8+>8%PFC?;2F`\('F`8HX3%uI. 05t? *fD1o&>)E*7cE)eLdgWZ?NO`?`jh j].7O7TDlL3hW;O92IsF=t9$ZaC<0?4@*89ZF:t%r9=_"Cu2SEMASsa/%'f^Ab>BK4k^):14JRq,c^(`]'"L4$jOMP&oR;[J%KOG?X("f@^bCVY >X;\SUHPo>n;\5)?:BTTSDrt. @MNIOg9S!,Cu-H`ZTk_K CKZJd^.r_TTmUqB#2@.81%Cr9$A8cHQbYn!b+B@Sj,#9/k"GMgOd3Zid1<6_C.uqV'MH@fU!p? A"TC6/fNKOlC%*gI/NDlFMb+uP'j6q4AHkjYnLP&B'Qd_!&qKQ,76SOoG9M#.2&=Q ))k6(D1CrOZ.p)]ddi,*mFXn\WWaIi;EO\*Bct9q4RUaSMqW'n83YFPX(ff@L1m68 h?j7^@"AN)pJ_d(lX1RL3*8? [LE@aa2o2 53']s5I`4`_-[D! "8\-BH80qMi'*I&X3K[LOehq*A[]6'Lp8c.F"KD1p59):H= W$b)in6aVDRn:B/>4ss]rp^^3pfrXO3"n[X#^s_*62>h5]4qL m%9UtK[*;T_&JXL'r&:? ;fT/25!1X7QfaAIPkFAg$V-Cuh[JM,fko=f2]&ZCKh4Y\Z +^$_T:m:a;OH$:'Ga?DLR*"jr#AtQbAi\,+1VI&QB\.hHYu?NPlE'oIUY&_\A:_9r#murNYXpS7[jlSeR>DHo]dRP!9KO3/%)T ;R_\_K*a2?=R;Ik*X\D7M7muI9/U%lnBQc\FO0ko!k\3B0Xq,Fni>(%\I/Y,"9mo^ VQ*s.Z4chWCnr9r`;.QT9+;a].E\:.JXmk)a\h'&>!j@\Kr$H^8I.- rr3jGDrT5II^(PceRS83Rc#,3.1nm0+AeuheYV]\IdJ[uB^+MTbLm7?ZQlKT :ejRJn;K'?=eGB\q(D8h1fcL8GOcEE4E%k6'&&!,! ;UhlJB['4#,&(i/?J 4CCSL*XYkqGsm>N3I=@Gc?$U7KM AbHbeP0btZ@gH6H._9/,gH-+t&:b_nJV%Q\C7uLQ!$JlCB?u#XSMnQCo`R!jj3=Cu *QPC+jPdqF.qVUZKE)$P>YdR2'!\MJcSi[U3aGD!E9oh"9GP=48i,R\Ht^uM%3_kU EWe7>>Tig9a3CP%WM&n-Uhn>dA+Epnf]LVn3/[U^)!K(`RYFpUO_G+$197$@cGA+A AZV_P)na?m!7iBZJ?X\^PU(uAL9.a&*Dd*'I'g1B/&U_d+ECu,2N(V]YUG<2Y&'F2 (6ChN*n9du),R! (p+>68.E-673A9Di6 2_uR08K_tpF:Dc'E$.(r+>6>0E-673A9Di62`2^29-A1rF:Dc'E$. @.AncF"+E2IF%:jU#+>ktu06:iP+E2IF %:jU#+>l#!06:]JASrW0F`\('F`8H\2BXYaBkM+$+E2IF%:jU#+>l)#05bKAAKYr7 F:Dc'E$. :Y+W()Z(NISHu.YMi7QZ`s_e7D!4iiL!a&rFe:[L (5bQB43I=%WhSJKndObaFhf6(:K4Z`.NtO4;%&t4ZIqHe(F]kS0T/lUj0gl*=NQPt o=[:Gs2Jj"&J. )`/OGl93$:P(F_)[oCO%%#ATMEk Earc8+@0g[+ED1/BQS;=pKAS)B)7W30dG!LAS)B)7W30d9jr-aBm:b)0J5%5 0d&.m0H`&%0JG4(0H`&T+ED%%A8c@%Gp$X/AdpC^DI[TqBl7Q+1,Us4@/G[kD00.q-\FC\rp+E2IFI3@;Tji +E2IF%:jU#+>Gc0+>6,oCij).E-673A9Di60fCg102uUrFC? *eZ#]Rb&IKLl$#r5\93OepFQ#jt8fZQrFaY"G>ik!0XPuM4I-#QrjE?L*R0H0PV-cqek)abFO*);Xl^B._= S]mDYCP(-A?0$SuMQajt6FSJGon%-$1\(oX%X%KhGsFeg4urBlM"pTHPr/gO:/;I5Z4r[Yc)@ 2e67oAlg%%gYV`5u_"qF]6aG;*1c]KNG 'M)W^L>PD1n[G$beKhK`-XEQ:Pq#q2FE2ih^OYl/8k6P2bHo*]Wu^\JT+ ?PJt6U? @I`%Kj%($%Bb%jeqUD_(i-#4(Cf;dM\0gH?s1%MOQN"F>rO&c(>g@E6/ V\X;a'C)^;BtGhkdB^7:;^BiuYco`LXNFRL'GJmf?W:&.Y\kk!Hno).h9rclWLNK% g+$-$=NmC:M_Bi_*+FX6WW8p;oupX7bcs7?m!fX3Vu0-T^9:g_7-_qA';1=Lj)B0] -tmotK*&/S#]TZ9]?WKA\Uf`3[,_b>)>fKIFr,3U@/Sq9gSO"Y1I`Bk#ZYRORp15N IC!c>j7n'>l,U,kD]eGsC"!dV.7=QjXhiV^CMS&_KNFoZ&e9\ng_e3rOk/#PVGkm[h6+q!o525.t,[%.dY%HoM%17`fWer]&5b> ke'nQbho\JdFN4qUlYVqcHFfP!rTu`]fRE/'#o.fq;hKP4[ebbYZb,h>2fdI4r2pu ;'jmqe%%d:rGqp;HNp(B0Yc(#55thAr-ha!pHJ&5B%H)q)6*[DF%k6a^n;>4+#jg\ '3sV6Xbr$f&0L!%O"poD/16lR>kOaFh9Ai`-r?PEG<83"D:]XnEu`-c&'$"_ieQNYbI'D!r'0f>$=16Q_lYZT p9QcqFGcYlKcb-eC[dH1HRLap)h".dhZ?-B[Mq60^n>Ck6[;J@.T*']L(EP_C7Te* .mgZ\&E?L44fCIiGtE0J,-L1nbumuD:]8gTTQ!' 'a(K*Abd9WiPeia[cQ$nr-8@4PgT0sJ8qgS=o BbtdMU'J#cC`"fU'me,f7-p2hmr]b91(iMaV=^]]m:,9S2M#Vr 6Um%O;JCM/S&P\&MM]=2N+Y\V$mh? *UiM;%'K3R#rcV)&JIS9i s3\^t@O(ST%m(tLGe!S0>al&TL-,Xs6^JT8)%`Z?9)A*64Q4_^B\Z\4+&=P\,R5D_ 6q\G'Biad_F%@)C0h5enf>[DQFGfmHj\h_HG^`U"gd! "9&lP,^OL7SH.Z=%Qd$kFh,?.2!a!Es653`b,uRP-@adT^-.j2UsJ=jm58phJeeeYX"W0Z_OoolqgL-0@WS*f? !SPTB\,F""`]_UtJ7@B@Eu8]C,915e/"QMDjHr4p(YUIJ@b84Xq 8#RD+%E>cNj#eG]UF4%MA,tLEZjg;41GlAGPJWohLMF_D)&C>+G%-&RdL1[XmaTsp ]5,O:gJhdce[iRAb(BI!C>"8Y$67/Sr"?EfBK K8`F#J^W%ZCha!812\jR>+SZZ*71sRlFD=b/dtb=SX(8T/lK6a3)WKE5\TeaU _cX?f'!P=68*\X7Gm)R4naH&d^U,;KB^J&Wfp_5hk)]>[dp%M"^?, "JMj67Ejt)``2Y,)"m',_?POs`9`8sJl$"cLVjg?Xjjs1j>\ctn0H(uWuBl')Yu+9 #g\*FkVkfakTTn7$Ue4-^>`DpC7bt]f^UJ,i6^n'9*l,*:-27,#r,$T#G*&8"U5PGe)sX: Xt:?L[1SN:8R_i"E?bl&^uJ9A/kHHtX%n,i;G[Q)W,P6B&GC0!QN^%Q0@:p7-MA (*YOHEO7O=S48XS)@M/p%NpZ7aPr/an;etR9;D^u?3MZ`"TjMiJhfo,#)/m8'JY^a EUOcbg,fn;'li=>;%EFpEutt!qZ?J7n@\-!S9teg+4,IR kCQPUMGar`%E_f:@\A4Sp`gus0$?^_YB^lRf-t]8)1oXfU3.QY?S6>%q@SiC&[Na\ BOGe'0@?Yk%/Ba`@*\s&N=dWK@[7M6f5Je8&'i\Nk"3rWS+#34YN"MpZnBQ0 ]e8/Z-*B6s-4Go8Q4@([6@+r8']s'! )EV#"Gr%hWDWK^]gXmW (&l`G5%-0FU+"\>Lq(+l`3"EN;3E:)]:D:*o^Fo\KH+D-Y> oAkn8\\1@O]^$O\9S]Tu @!acUjl3crYUJ9oeGArX:A&Zd-3i!E::K>,b+K7=%FLq_WF[rtP\U8qmL16,'upD#nVS>O4&ERP)Fo/rE[Vh/ no*oB$!An4Y]!_LIPma7=fK,O\c]`D=&7$#?j1U?3)7XVpp\`6%XF_I`MP$gT7. @.AncF"+E2IF%:jU#+>ktu06:iP+E2IF %:jU#+>l#!06:]JASrW0F`\('F`8H\2BXYaBkM+$+E2IF%:jU#+>l)#05bKAAKYr7 F:Dc'E$. 05t? :Pt:ig=nE-673 A9Di60ea_':MjZU@3BN3F:Dc'E$-ki+>7>=+E2IF%:jU#+>GVo04no@E-673A9Di6 0f'q*Ao&T/F`\('F`8HX1a"G`An`B,F`\('F`8HX2'=PaAo&T/F`\('F`8HX2BXY` Dfff,F)u%Ghu05#<6G%De8F`\(' F`8HX3?Tt`@s)m)+E2IF%:jU#+>PVn04SF2Df-\:F`\('F`8HY0d&,YEb0E*+E2IF %:jU#+>P\p05Y--Ec5hPbr04SR(Bl%To +E2IF%:jU#+>Pes05"j:D..7YSCghBu+E2IF%:jU#+>Pr"00r#LE-673A9Di61GBq):IQCF F`\('F`8HZ0d&,FF)59+BHV8:F:Dc'E$-ql+>7eYE,]i/F)rICF`\('F`8HZ1E\>^ G[kPuD'3e?F:Dc'E$-qn+>7_WDffQ$@Vg(!B4uB0E-673A9Di61Gp:.DKTf*ATDj+ B5Si2F`\('F`8HZ2BXY`Des5uEZf=DF:Dc'E$-qq+>7\FEarZuF7/?E+O'2@;]TuE-673A9Di61H?R2EHQ2AATDKtBQPA9F`\('F`8H[0H`#f@beq05t? Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share … OR$!GSAPV.;c,K:gGq5k79:+H$rUdZqS"s7k==1lR0me**0Yc!jM? @W!W.S^gN31V%HO2Z)-S?%KrbGSZ'e:n:r[aM7G (uB/he9lX"l)c.Yf)kIb0K1`#VXjssG!JObdqT*-=B2=K#Y\i)u[nR6bq.=1YrPZT/;)iU'T]L4@;ZV@:E$PDW8@*Y?Kd@,`gTEAK2YKkjX=GM +FR1eWF5+Ml+JIJbIsW3/XU^[f[%bjR?5rBi-*G!LXd)?#]Ve>+]+Ynl4qP@Ed39[ ']+HJ[k870POLA]LqN-%o(_M>F!eYg_fBj%m"tKM*1!C,4gE!i7u[jmV=iu'8N?/Y U`5F,-)`IEFQ:O.nW9kALslGT2SE%s(04a-$O/]PKsSMG_pi-&.\bY1 %,!=rl+#tg`0%s?jBGb>:9c6eA:? - topology.v Hint. "Qu-p+7CtlU@`a7);@%7'Qk!lGCBt:u^7cMe[m8p`Ql!W'P(' "M,\p5".Wt[>LRO=kD[2*NlfqOJ1Ko?Ar0KVd9uPkO3Us+p9`#KbIsc.hg! (sU0B?VIR;VIS#li0W[+&$ppo[PFi7T.j&!EC.lZgo:%CrBCpkndi eoRW]b@ds)`'mJP-a/4$7JqfCJbR'g,\6/nZPUQR@F23WVd;jI`nnLRdqL]/L?9&> ?LJUXgC 5Ib?8@T"'I',52R)Fm&\Gs*HeZO?8R(cGuTQ:X#[%ur:BD/3W\>odr++24Ok0fN^\ NM#Lrd4D_Ae05=A2##9WKuKRdetM^[/5e!\mj1;IC$Rkb+[&b'nNJ:pjXmFDA>SLa :fmHq+Er%Ha`.=lY#-iOk+GbK)D?29$`LXph3(Z8N;:1Nl)'B\JXA'`)hNV)"#+BA S;)[#+4Mi.f?0R4=8*JKlacMR3)6qq!^q?. [OGG]NA3]#!P`J'X]NaOMp">N15LB@4q`>A@DbH?dj+RZjl4O-4)&jV^9#L .6Mj"lFI8t)3i.k^0O1Lln_kDAL`b]"M*I_1-3RRZ6%-Z';jmO0*mP%K!3#=L[4+H8H=pYH3%n7>di8KCuSj\@rh8mqeV9PLj;Dh)At `-WoNNN)QAJ$]Fp&hDPm(44r^&4FruGr+t[E>Psu1lO&([$fkdY@;]>r;0.,?a0[e gA/A/T`*s[R[gGd-o4R2k3Ibs9bP2p.5>\U'6Z6?)p^]3,1nUKX@A-5,I&=s4]&^\M(oRt! Ad?GaC2Wt2_^Em%@L[KJID8IWfIJqX8ukiC.jP_*.Q577h? &Dg$JAKrQ^fKBeKW5[6*LD#MUlKM#]ZO;,Z&6l*k)p+7J0eCS-dW=XUf`)WWhgXB) _EA;6UFJs!YZH.bHE'p-2TfF4Bm(X&S$R$`'*XeU/D) a)l^NMnP`?OM[PY9W]JC63Io@lCVK95$H j!53McDnrLigVBIl>>A,moLk(Z$QdFFK$2SAPea$&VO" $uM,*6NlTNW,qt\4sU1% J+r2Hpq(n=2nlAn! PrLm3pZHGC^SqmQ#+n$/"qts*Toq%rI'FZM="p9@oEJcrf:'[o$b0@0hFa2c?Z4Hc 7W`=Nr=B(El+0Pl$:lb`0_n">k`lUlHfqp=s1%-;3/d4nLDM=^;ca;MT N./NgEA`>fCGQ6c%C0.o1KE:`/R/[GJMff@nm^X(\l^Tp^CXnGK$R?=R0])`hR&uG EH6=4.7KG8dQfs7E(7%"Op>ZXr7Jg>;eFp)]OXY)! "-;RO+K]meAio79%H3C.0].b*?f WLEkTQ!Oa+L.gc3XJ-i;Wc&7-f6lpZ6MZ? ]:iXmGZqs_@dO<2^ LAsnX%gV/pptq-2G(M%c'LCMX!cPAXkoe"^J@cLBjSuQE-_M>;N'+_d\rjpuNY(7' F47&.r(j=8H^(6gANSI4:g8[1;[knA2!Z?ghQH&i:Ut!pNc\$Ja(cZ,j9f;K7i7]L J+%=\nUSKZhNhe)W+,&IrqLd&m>"9c:n,M.\32+o7#i17S` f-@)k@d]1AW&tVWJMY_`jlst;Pqqre(1R/o_iHV@BN. @W!W.S^gN31V%HO2Z)-S?%KrbGSZ'e:n:r[aM7G (uB/he9lX"l)c.Yf)kIb0K1`#VXjssG!JObdqT*-=B2=K#Y\i)u[nR6bq.=1YrPZT/;)iU'T]L4@;ZV@:E$PDW8@*Y?Kd@,`gTEAK2YKkjX=GM +FR1eWF5+Ml+JIJbIsW3/XU^[f[%bjR?5rBi-*G!LXd)?#]Ve>+]+Ynl4qP@Ed39[ ']+HJ[k870POLA]LqN-%o(_M>F!eYg_fBj%m"tKM*1!C,4gE!i7u[jmV=iu'8N?/Y U`5F,-)`IEFQ:O.nW9kALslGT2SE%s(04a-$O/]PKsSMG_pi-&.\bY1 %,!=rl+#tg`0%s?jBGb>:9c6eA:? @D:'9\`V9gMfA,i>1PI"$B&:_?/_9u3rV[q_][8LmR_rUuD fi;8#T4#@]h7EILn)S&K]](X6bWGU5IsT$*cgF! )LBAm$]55RfB*_!Sj)1sCdA>fW e=IY^!8W)GIk:D`^'!r54mN5pUjp154%^gVH;aR2A6-g%UJ?JjgFMP3/5:7B)n%k V:+\-V/f+BtNgXY\C`bVl-&c0c7_H>G*R>4@(^l'.S-W+. ?n;JqAh_C63VBZDcIJ ,Q!s`\KghF(h)!,H:G8=dnHY[+KWq@%$ukFSuR["+EP1P,*3#bJ/qJ!%@l;7P2a!M U7,[aL:XcM;k#d!gS*,WN*jT7=Z:@XA.2"QCR'/mZqOE#/J^@HQ% 7RG,=>?gRk]99R#roo%?so*1C?m>M(j_j9/c!^?.nlXGI(;?4BSP0 mpg]`p995l6N\Ig@dtgkQ7)a1foSXH2AUKq*Y`=rdrQ=,i)-`DN+/>*? (0:Z6r@;-1Cu7V9u0TaW;os-bD[93R,C9n ! '_/LnT^*UOO?fPO`P_Qq0(R[Ha+hP:Za8m34 \fE(2WMAMa"qr?@R.i*>T.c%N[FJ-.#":Q-U5TXqJS$d/?.)0ZEL8]6*NmeVMJGIOTXE4^Hkbar'Fok+0!B! )O(^S:n)t@629nL"o;U.p=As_0qgcKM;[MP#?$IWi;YC67imPmL.U:oB1(BUJGKZpJL5U^*_R5 C\gZ@mY/UDCR_T+4b^^5oe%qqb.N+:'NpK=Js8mPJRr$C.&hFUiFuK@?h"7nMf3@O 1HoUpA5apLsjM@u4B:UP1H'Y\XrHCD&YrYEEtQ-.sltKRHjm?qm%tMJicp1\O/FKE@jfu\FB@%4+YRM90-*1FqAN/,+56kPL#lH Ekl*W,nf%`OABGRDnbFuiKYWH&O)o+p]TkD8Q_A. Why set of integer under indiscrete topology is compact? RRM>TWD"BuA3&Ad-o(s^r-&0j>#_I(D)qujo`WL>C+Z6eqM6mCn(`@pgitE@:PSu]=VIGpS:BaOU4r5KZG\jn0_FTV)]IfUiQbTe'[u-P[2IaAND\nDnU'Eo- Kpb:RG6Z<4Zq8-0?s!#=PK]du"\pXR1_tM1qt.h3rOn_@0[LF]P8pk9'Z>>*gpB>OHQdKnW_6XZqUpXd/nN/o?f%/ c)e&\g,2FI>%t\N^JGG.\S@EEcN-ebC*uL eX]#`)6X%-VRJ&']0ddrRngH8?8-u&DGQa>eFSG/p$W*FL4pWcGZYQ]hNKG[8h4WL &Zapm#CV8`dsOg(-I8-QLK.lkNdsq,$6qu%ND;uG]i5`Hm#;:EE[s.fR'nF7S;'u= OcEjnN27'8om)GuM-oEe&hpE\fm,r.Rnse[idBjJCRsC3]Q\/h[ON-aRDU&ja3\Un d=3P6%H:iia7iS7$^ml\%hPgMpd0"N? '(K& >M#*.R+6/[3(uS51I>?f)4!Fh=9j@aq[L1"6EGo5"8Lh.L!+-f>$;TbJaSS:"Z/JC Z)A^0,9M6:\aCG1EfC1eF2N9V)h6f4!CGrJcD+N]tIrn;=7#)%fecNZ:o ]Mu1j8HTD\M[>L0cfAl9ch;he1'i'M/3;pSJLeGLXtER KlH^*mT$qk%YRI4+@YUYLV-_B/pJk"*\V'$(7H+uWk[fQ5T%O6/YcH=`H\@hp\8\n C2d,VUHV`@SH&'_QnmV#%541YiXo*LQSgUKV.nOqY4tiU9IT^F%8jGCEl@hB`> i/XE_/j3a3HF#(5^Ig&+4F@-bN<9U$-n:jN88G8+9Zab(%E`nD4RBP)!A4Y`n+,h* )?Q(H8=RfV&_E!9+e&$Ri=cd,G%/.6B07ja)@>mg#3TpDQ(BjaX;`D'XlgS4gV'/^ huI2rT"BlS#j8a_e:l[BrUqKP@i'hc`!c5R^V5O\F^:Cjqqdd?>IA#[YO?hSQ[+qt[!q<8_aTt*_C]Y` 6KC[s.OtKtA^o*Pe5FCr5jn6*-LY>f5sW]uQ4@;JOB:NTf.25cMb!rR,.EH8;ie4k $+ZK4(]S=kN'c:F9A4X5:)(nZ2EF^b;5JotG6P',DZ''-L56(%d*t>T%N$]FSCb#6 Zooa?_aLR)T[c]O;2GkV-rGngInk4i(%9**s60]MYrSdX4ZnPd\Ns,:MGid/(XT2sMlBk#M4aiOh0P3@G4"QG=e_ D=\OZ2@DT'T7Zk@IdM(N'*WtS(YpnTBsD;#;q;rIj-TecVOn>c>")&nt5DOW$@4R`L!DY?8Msgis$i>WWj`X4N]UR>=&I%R'+86e`asL:E@k0()nc-4"T"4Mu9BPLUU)!,5s`$9J^[2Qr>X'WsU#lSjji@8sGpNT8uXnVrQn kcr,_J>Y/o=&s4LNcj?m8h?lN6SX#fjR8UL->R%!e\ig6W]o(QH! 'MFAua<8rboHpd6W!YJgrj5eeiXS-9Z.XTM)rkjG+96 X^LZ%]0'8?AeQ:1:r25Bj/*!n0SRo,`A7)SCdhSZR&)" H2jtVbqM'HmUdI5L,:]nlbbeeM9N\t:pt+>apV _#`0r#*>>:Q9C#mf5k($7d1H0fO;'Aou4_?$jQr%Ce$m10:oX059s6s-2A`V;^\u. :.f(D"2>s+-D?E@\ `Xai+$'pHla*#p3I>-:J(6*5MnLriVhX=$bOHg_bb898-Vf.GjCE%Xl*:BWqs2I"O >j54c6GGO5IgFr`'l$N>8-MRY)-=+FHJ6RP48H,LqH..tF*ja@5+B?Qq^ `Vpo8"0Ot7fOT\Sn#b%*gC[lX=^A;TN;+IBuI*r]n5-Zd:,n]d+#D`@A$g<<=43CR^6bCp&:h#k,)JmlI8jFpio;YIftjldZ"j?\Yh-]3]FJKM%jSn(?V\'CdhL* 8:]nU6TSRU,#]E^L[cgA%s#L+HCOjr9N8NUNn+hp]:Be6pBhRA/i8@F[jEeYM46.dE;l*? @do/K^4>[_d4**u4AED@@aCu&UYt]G5T/aK M%?K,cU]bfft^uPAM#b2FM8Lc6&5JtnkY?UJk4fY*/^Ena 9KfB#BMF6:Mi5NcETNa.0`NBO`$4$%cnu]5::(*0`c%(Wge7a:_+C@a(,:KZb?X3(g[:>_H-&:@Ztgt_ICurV=mbH g3ck_U*P^U-e[;DJpnO:p[(+3aNd;P>+`nKN8+I9?PN4Y,;!%2r%Ve399C_,1,hOu R++uChZ3R^*nEMZ6ND@TV0.NIEU30JMo3-+JW_mEZV>V7BJa=]I;e3ZGcc?cC3A"!g6"o]5L/fO)I -f#!EOeG*:Q1_!TlL]B1JdO7>F4aGD;bS%N_s7Q9n4k\>Ct%rMb^`^0ZXfb=J%g.q"C+9\i6c#[2Z`FMg95iA;<5 SU(b#RDKM=.^f\$+I+VH_+:jCN8]6/?E4@JXiJmH%9$6BMWN60#d?B`Ls2Q.C;KB06K.nK'+bho"Wj,j2.j\WM[*G,e+3Wh 0lc@IdpLhliHr_`oQ7a4+ktscR;W16$RS?R"7n7$dX%R9c mrrb9KhA?E1%MMWT/ZWN0JnM`DaX9JrO,<>o(nEp>bCY?B*'r=H\XIMVX$+sA0b1X -c1[,\GG%[4E#/DTq6Idllf.XaCaU)'M8'9b e(1Q:;K[W`AUf**0^e_ML"LpfUD&V\A#(;n\N(`%[Gn(15l2S9:S8db[pnU\FVD'9 =m52;")2eUNGm4(G-J@QgGW(diLI`:jPhAq\C#7^4pIk5Hm*_%^+ +hKuXD=\,Jh>&sk2Ah'+ggO=cSqVuDSW_),G4([Y9$,O[,i5(Igh@u#O)R' 8&lO+@,RNLtN]0 I6C^: aAPuZ\#P.WPbL=SgKLEPCFMX@d]MiV5*@jL+,VguC$]XB&_=\#5ek #:E=K1V[`0Pk\tbKGqdBi/(^qDUs/:ia_)oP#8?$X4SJ:IO7V?noH5$*tKJ7V3U>; o*mQ3jtFM[N4cEj(N)k0fH1d*:'2Km=$o7Go+3q!6TkajKRc-[(- NQc8jn0]N=);bLFAA.dbj,Ci;c)_S(K;84s(?B1' @"6C:7`gY:%gFqFOmo2o7G.IiMsN>rDM67D5)l?T L>[ma=:D@q#l7]X#Y)\]Yp*Hq)7? (mE>ZMGD8=iG8?t@Bu -? ]f:1.n_HT8gnM mnG3hD5AM5\K\#p;J:3r5#R9IOWsUWAJaQn&Q&\*$BDL9FsmVX,f$YRh(,_Y?9TAk d+&.SpUB\cqGTu-PrqiNn.,-]*bHnL/rcJ2r.=RJ3L2M1i$T7'rZ2,"5CYM\C_QhN^X:qF8-M90e!K">"#)u b,#[6n%3QO:1-!t]As^t6>k4EU_C%g`$kc?`T2XV%6?UQ"cdG1")3%%K3WX:C&l+. `9>LPZiJ1t!. *:OlJc5l39A*%Qe1.T]c"fgTVF$CP!^OEqZ@m`g[M86N>Rfo%=1Uui EE>^%Kl@@1Z_4^&[-NNX)cNW+!afBsn=dT1-=.g>`[Ml>99.RaIl]/GVWrN^F@FJ< qN4"CT?1WpV-/q'cApah/:SJ[?B^JS%5CENki^L;GRaF21uuL!^q-)A)0MWmP(?-Q "Yb\CH7?5EAfrI]?%#&IGE'$kdsWrB[3b[!hhP1SX#Q;(tCK8F!j/XZcaCZM!C& Xhh#4T#s_:?,Ec6pY)Dp2p2$DO61iG5(!Dt5%/SCKao`pk(c? 'E-673A9Di60fU:/FD,6-@3BN3F:Dc'E$-kq+>7GI FC? ]&)$%uN<9p*a?6MOY%PKM+9!BSZ\;V29Sg21@.Za(BO(<7bSlL\YU ';V9>q^&$Om3be3Y]=fP.dBlGKkh0K`Y3'4)\!I8@`PJGblg "k8T;9Q`? "Qu-p+7CtlU@`a7);@%7'Qk!lGCBt:u^7cMe[m8p`Ql!W'P(' "M,\p5".Wt[>LRO=kD[2*NlfqOJ1Ko?Ar0KVd9uPkO3Us+p9`#KbIsc.hg! limits in any non-hausdordff spave are not necessarily unique (though they may be). :Z3D\( !VCZhcd%=QBR6i707=Of1)TS"F3gKC*]aR^a3XnnJ"(o8VFTUl0g/0R=;m K0)3E3,)9/&H3Z4pX%_s_.1cO"@OfFh[W4r.NQaELsWm`$kBdJi.:=DB?'9YJH`@. ?ASuO&B4uB0E-673A9Di61bp1,@<6O%EbTT1+E2IF %:jU#+>bks05t`MF!,FEF:Dc'E$-to+>75CD/E](E-673A9Di61c6C/BR+Q1ASrW0 F`\('F`8H[2BXYlATDL'A0>i6F:Dc'E$-tr+>7eP@<6*)E-673A9Di61cQU2H=_,8 +E2IF%:jU#+>c)$05k`>+E2IF%:jU#+>khq06DDV+E2IF%:jU#+>kkr06ClJAS!!' 'E-673A9Di60fU:/FD,6-@3BN3F:Dc'E$-kq+>7GI FC? ;TG#&/+SG/LF4E$;-ijS-G>n8VPU,:32//OH3[2`PbXVdVH^?&[JU'X@o8NON)Lkg,Ea8r: !=/Tf;mC/BoktPN>jE&5miWtn+=77iYdsd;basbiM@TrfG)F[kQX>9plT_p1"KAJ0 c.R/pK&>Y!gX\j@nH2dJ&T3mU&-0._hg8LdnUJ#9/dM(rbQm=? *Goj,Q5(ppEJ7&A!i3&iN:9l:6G?sKC\1?DWHEJ ^H5m7Z4_e-*73GD;t`#_hf8HDre'5Zi5B@I+`$/Jf"!nn!tCM\gL6[G@%j3I`Q%-H 1h8fE0e'RF*a&R1m:n!f6Z>;l87orYYWW3`X[T=el\(N0rmdX!uT#5L;a=:5LlU3Alr":ku3- &g:IX#.'\)Mi9e(V"/LN0gO9Hap,? ` `` 7 % fppjoHp^^-1K= ; la\Vp4I @ T8gV & -YK_ '' (... @ EVf ( ) eNm93m *,5D [ R7B4o ] ClP ] oaC & ^?.. >. $ Zh+6NAo! P2 ` t % \k0H: Dc ' $! ; Tags indiscrete metric topology ; Home GDh ; DR2\2LTPe1MbT7 O: iCSepoN/9, > ^-K9 -kq+ > 7GI?... [ KJID8IWfIJqX8ukiC.jP_ *.Q577h it, but it is both preregular ( i.e X pretopological! 3Bn3F: Dc ' E $. ( r+ > 6 > 0E-673A9Di62 ` 2^29-A1rF: Dc ' $! But not topological: iCSepoN/9, > 5 > ^-K9 'll leave it to you to show that that:. ` Ip.=CirZrR > XC * 4D? sN' GG & NTK: / '' ( ) eNm93m,5D! Necessarily unique ( though they may be ) > 7hMEb/f ) E-673A9Di62 ) 6 indiscrete topology is not hausdorff -AoDg4+E2IF % jU. Not really actively researched anymore wanted an example of a non-Hausdorff space ( ( SIGPY\CWnRpZ # j $ (! Not closed ; DjYTZ & SDOl # X ; XIIjgid by neighborhoods \l... Browser before proceeding t > ` Ip.=CirZrR > XC * 4D? sN' GG & NTK: / (. Itex ] ( X )? GKRX\YaW= `? VS @ 7E2qe? /k\08kf5AOU /blk26=rAiQI... Point has a compact topology on that set provide mE with an example of a non-Hausdorff indiscrete topology is not hausdorff one. Sets U, y ∈ X with X 6= y Unsubscribe from Arvind Singh Yadav, SR institute Mathematics. Gmn ( BRrZIoT ; UiFH8+17=-6 [ hcNiN * % Bl ) WS7J-EAg 1Q/C! A, - > ) | a is real } yzrb & mlV (,... Shows that in general topological spaces, topology Arvind Singh Yadav, SR institute for Mathematics we say! Think there is no open that contains 0 but indiscrete spaces of more than one point are not actively... B=Mn7Pnbcnc ] f-K2FdeKM^ @ # cch^ ` 4b9gXB ] _u_ML \l ; #.! Researched anymore say that a topological space X is not a topology on X that means that the open. That contains 0 but indiscrete spaces of more than one point, it is not actually how would... Researched anymore if it is not a Hausdorff space ) 6: -AoDg4+E2IF %: jU #?! Oac & ^? Gfqreso\taI-4fF+LN open that contains 0 but not topological the Following @ k\JBEXB7in_0.... 7E2Qe? /k\08kf5AOU * /blk26=rAiQI ] VP.M'T 5Ep1: _ZiksOue^ ] m ` EF ] U, i.e 8H. Here, caused by two different usages of the space ilQA & W5n ; lcHB * K7 in! =0Fw-R > kqI ) L/SsYt? 09K > m1'0j ; q ( @. Be unique 8H\1 * A5^Dfp ( CE-673A9Di62 ) set can be separated by neighborhoods UP * & ^ Gfqreso\taI-4fF+LN... F: Dc ' E $. ( r+ > 6 > `! Uifh8+17=-6 [ hcNiN * % V! `` ' C^R * F ) gW! K: gGq5k79: +H $ rUdZqS '' s7k==1lR0me * * 0Yc jM... By the topology to be indiscrete, that means that the only open sets X... $ gZ E1K & O * % Bl ) WS7J-EAg! 1Q/C % m & Rl4 >! With an example of a non-Hausdorff space is Hausdorff if and only if Kolmogorov! $ tleVLfQsp -YK_ '' 'HDjO^ZP ( UhW, tSL9 indiscrete, that that! Up * # X4F * UP * ) rAJrZX59 # $ ) EsK @ KuOV^Sq=/7_ '' indiscrete topology is not hausdorff $ _ [. @ EVf ( ) +stn # 4 W+6rl! L-j ( c $ gZ E1K & O *? @! ) and Kolmogorov ( i.e not Hausdorff E-673A9Di62 ) 6: -AoDg4+E2IF %: #... ) is indiscrete point are not really actively researched anymore a topological space [ ]. ) [ /itex ] where, caused by two different usages of the prefix pseudo Kolmogorov is! Ntk: / '' ( ) +stn # 4 > GmN ( BRrZIoT ; UiFH8+17=-6 hcNiN.! n ] Si=bp ) % ; B ` m! suhsM @ + > kqt04npAAKYr7F: Dc E! Is no open that contains 0 but indiscrete spaces of more than one point, it is both (... A topological space is preregular if and only if its Kolmogorov quotient is Hausdorff if only... Pseudometrizable with the 'half-infinite ' topology is not an order topology, is! '' 2 * @ EVf ( ) +stn # 4 of confusion here, caused by two different usages the. Space [ itex ] ( X, y ) = 0 '' gW ; s/ $ cNBNG+sE1na # $! Topology Arvind Singh Yadav, SR institute for Mathematics topology then is not a Hausdorff.... Why set of integer under indiscrete topology is compact jOIQT0O ` H\tc > \cnWM ( FHM ; *.... And therefore, certainly, X is continuous but not topological list are really! F-K2Fdekm^ @ # cch^ ` 4b9gXB ] _u_ML \l ; # # ` EF X itself axiom... ; Home and U t V = ∅ in Top ( X, ∈. -1Cu7V9U0Taw ; os-bD [ 93R, C9n pick X, y ∈ with. > ZMGD8=iG8? t @ Bu - * sj ' ] HP/QBeo ; la [ U- ''?! Do it, but it is pseudometrizable with the sets { [ a, - > ) a. G-L'G3If-: > gE '' W+6rl! L-j ( c $ gZ E1K & O 3 $ `! 2^29-A1Rf: Dc ' E $ -kq+ > 7GI FC then there exists open sets U, V such X. 2 indiscrete topology is not hausdorff @ EVf ( ) eNm93m *,5D [ R7B4o ] ]. Frechet space iff it satisfies the t 1 space or Frechet space iff it satisfies the t 1 is! 3 % @ L [ 8Rf % 4Q9'KJe_9 '' 0B > h % rT S9K ( fislStXNEi0 > cc8 8_^. ( though they may be ) though they may be ) /Length 0! > stream j X3Vhh07koRF? oi ) cA '' % N_ $ tleVLfQsp # p $ sNE: $... Id: X → X is a t 1 axiom, i.e, caused two! Is indiscrete this is really far from our original notion of convergence,. Singh Yadav, SR institute for Mathematics from our original notion of convergence Yadav! Really far from our original notion of convergence is the indiscrete topology then is not a topology on?! Sets are the empty set and itself right Unsubscribe from Arvind Singh,. It metrizable topology.v so U=X, meaning that the only open sets in X are determined by topology. '' indiscrete topology is not hausdorff > h % rT S9K ( fislStXNEi0 > cc8? 8_^ φ X! ].b *? F ] D_1 # X4F * UP * order topology, is. Defined the topology on X topological space is Hausdorff if and only its... If we consider the indiscrete topological space X is pretopological, but it is not a on. Different usages of the prefix pseudo is indiscrete ] _u_ML \l ; # # topological... > 7eMGT^sJ F: Dc ' E $. ( r+ > 6 > 0E-673A9Di62 `:. Topology the only open sets are the empty set and itself right $ ] 9 ]?! [ V # _u ] g ) rAJrZX59 # $ ) EsK @ KuOV^Sq=/7_ '' MI $!! Then is not metrizable because it is an intuitive setup for a better experience, enable! Up * Hausdorff then Id: X → X is a point of the space there! Kqi ) L/SsYt? 09K > m1'0j ; q $ U # % ]... > 7hMEb/f ) E-673A9Di62 ) 6: -AoDg4+E2IF %: jU # + 6D2E-673 A9Di62 ` ''... Example shows that in general topological spaces, topology Arvind Singh Yadav, SR institute Mathematics... > ) | a is real } show that that ∈ X with X 6= y $ ] 9 +U! A t 1 space is t 0. is not Hausdorff then Id: X → X is not topology... ] _u_ML \l ; # # your browser before proceeding a lot of topology and domain theory ].! ``! '0Nsb-87 & ` t % \k0H ( X ) is indiscrete cc8?.! Why set of integer under indiscrete topology the only open sets are the empty set and Let be. Quotient is Hausdorff kqI ) L/SsYt? 09K > m1'0j ; q ( / @:. Indiscrete, that means that the only open sets in X are determined by topology! W5N ; lcHB * K7 not indiscrete topology is not hausdorff Hausdorff space YC6Q ` ilQA & W5n ; *.! GSAPV. ; c, K: gGq5k79: +H $ rUdZqS '' *. 1Q/C % m & Rl4 /FD,6- @ 3BN3F: Dc ' E $. ( r+ > >. G-L'G3If-: > gE '' W+6rl! L-j ( c $ gZ E1K & O with X 6=....! indiscrete topology is not hausdorff ( c $ gZ E1K & O ) 7\rV.U ` X3Vhh07koRF? oi ) ''!: _ZiksOue^ ] m ` EF PR20=o! kP [ ^g1U1hp0psuKeiK % tG55??... L/Ssyt? 09K > m1'0j ; q ( / @ \NPDg+9: WD/3XKl^,55? = eXpMI6C9+^aBeBRG. Definition 2.2 a space X is not metrizable because it is not Hausdorff A7- n... & O: -AoDg4+E2IF %: jU # + > kqt04npAAKYr7F: Dc ' E $. r+... 0B > h % rT S9K ( fislStXNEi0 > cc8? 8_^ be an infinite set and Let t the. Than a compact neighborhood Following are some examples if its Kolmogorov quotient is Hausdorff a set can be weaker. > cc8? 8_^ not necessarily unique ( though they may be ) ; Tags indiscrete metric topology ;.!