para compactness in of spaces
TRANSCRIPT
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E1-21219
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thhndty lic.otfira Int .n tlo.|.l ^-
@rebi( t h l s tltl. c.r.l !.ep.r.d b, th. U.tv.r.it, ol ltscomtn) PIEISE TI'IE: lh n.grttv. trlcEttltr cop, ot tnts diss.rt on r.3 pr.p.r. I b .B tn tD prcor or (c) . A"U.A-. 8rD wrr f ln I h.s a r.tdotlon ln A, Lnna 3.2.U, ch@8. nrl 60 th.t
by
h.3 & n-niU sub3t, \ .rd rst B ba sucha subt. Deg@ th ,,Datcurqit tulEtlo (th.t l6t th6 s.t ot n-tuDts d! nz) by !.ttlrE v : B - (nz )n M(p) B. bth n-tuDl6 { t{p I I ) I n , . . ., n(p I n ) &nc6 th6t! !F .! y Snlt ly r|!ny !o!!lbtlm.s f6 Lt O Now, b'yLbr!3.2.9, or o wfth l'l|oFtdE a(o)l r(o). 6adr p !D U (p), !,y
LDD! 3.2,10, t, car.t ot. o dil !n r Vl n V2. (.)r
b.n n-6rU srb.Et of B otr obtch M ltrd twoht daclnq rnenb.! lhen th6 podrt (q,r) !.
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W6 DorrEdfythd
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th locruy colrtable opn rlnnbnt
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u0.tu"61cr)lhB), {{"}l*.L0utlurr2,
lrl= {uc&)ft}l kK}, ald t-uttrou ut)}. tat u btbo!e. covrEflnhg v.
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ul u t 2 .."
d.rornt colbcttdr.. Dalrwts odctly o6 mbbor o( U l5 lrdeod Ftn!-Erlte. ttr thk Fodf n Il ard K. (f)r tlDllly,
Stne dch Dohri! EUX lt6s tn u .nd erdr pobr tn I lI. rn.t iao6t two, Th$ X l! ngtlcornplct . Nod thlt
could haE doftEd rh. tunctton c hdeponddtly 6
to \r6dt th.t I
X ls corDtlbly laFconDact, t t ttrdlx c{f} and ! a3 Li brb3rn tt6.t I ) a$ cordnd tn d(f) x rn lor .dr HUr wt ) unro.g
v b6 ! comtalv tdtDlto op.n covr of ]l. {vllrrr}. htosEr lnsot. r, f n Vr lrtth Eq..ch Euchtlrratbodr t =n. Ar atd !n E, un(f wl$ dn lnd (c). x . lnd 0) cO
un(f
so dAn d foradr ! . ! Ii U0, tol,
so d to detn rn !;
for 6ach w(xl
aDd cG), d(x), tn tlr pro.C of W(xt) strt
ior o.dr
!@d!U!rsly.!
Arso tt *'
l,rO U2 be
aE !D dF Foor of (c) . clnndre.t
& b6ior, each w(*) .r h
13 oFn, .nd n U x,
33
Fd o.c.h .>t, nlu{xll{x).62coE b-. t . {w;nvrl tr a.g nlnt tor of b* n>l
tat wl-961611;. ona xe v--Uq}. _l1,
Un(l,t).
trlnrEl ut({o,r},r) {l (1) otn=ttn.tEl (tt) slw! lll. E)r t.tnal fd son tsn, th.s6 !t d o!n. oDd st.
d ttD=tln,E6! lff oo t
rh3.6t d an lrngr4du a 16 I.
tosstho! wlth ti..
nd.6 up th. b!s.
Ih6 topotod.ar aF@ (.) ib) y r ktr
Y ha8 th6 fouowbs p.o!.!tls r lrd.t8o nana!-
ald 4cd!n.nst6.I 2';
has crr.lact!
tlerdoE
Y 13 nd!! Moo!! !Fc. cout blf b.&,
.nd d@r not h.E a Gd3rodr* or3 (o) Y {d) I ts !u.-I&!d.lttf, l. noi co!6cdo!trls ffiDd,
o-roo.rt
(e, Y k ntlcompact. (t) Y l! @it bly Frlcotoract. r, rcr tr. (r(6rlr. oL whr tollr. olcPn and rrnlG)dr(o)l dlo) ',rrsn,, and (lr, the turlcttor!8 6r d! nuruuy itrtdlctng );
tJ;r="1".N4re ach n > l, f
Now r6t l={iD f, .nd | !! ttr,
ana v"rul.J !E tsr4d. th .et Un(t,t) = ld
topoloslr y.
th6 Dotnts.d
[rln:rl u((drlr.],r).I;ll. 6r o, 16 flrE) !5 oe6n,
(t] orlo=rlnfor.6.
rorsorerrtr,
a n d { U ) s ! v 6 na n y ! t n g l
lhe sths!.tds on J togethor sfth tbe opn $ts prsvtd6 . b.rs t6 tne toDologyar t. rh. st c6 Y ha. aU adtIE prcprttes n6tr6.d 6&4t lor Eracdpacbe8s . thdlrg lor y{5} rhat y l3 not [email protected]
57t3 ellolos llt. to rhtrtng tb6 3.n I(5) rc3ult in E:6nEL 6.La. l. lot oouodonwk x(5) I !ro