i

f^f^U^gCr "Keovewv l a - ' ) X ave open.

' U t \. few\<i p t - 'V\^LUw , AAea(\\vv acK, e l s.t. xfeUxo

s.-t. c Ur . •

,Tlsov<?Mib. 0 0, X ave closed-

~») \/\<<*»V, ^; closed ^ M F ; clo^cl .

f ^ U i S open YeWve t o civ U;?. open Yel. ck.

poof-, f y e Ud, U.E") ^Ke^ OI.IXA/") < diax,\)') , "so ye Od^ (x . s )

ci.U.y^ < J ^ a.Cy,s/)r L ^> V f Od, U.£) Kow •. Oct. U , S,Ar\ c U^, C U =•> U IS ' ope»\ Meed-to sk)u\i: c k - ^ M .-i? dj-.op«. di-dcs^^i •:"z.,C:L-clo 4 •

Zdi«>Yew\. X n«\Wc Space., Vc X ?S also a vtlYiC spO. l .U'^V is ope f f f a v c y srt. V ; opeA (\ 2 U-VnY

. Example X r V= (1? - il « H c 0' . - . - V , . , r - ^ . - -^

£XQ^k i \l clo92c\ tf- txvt VYJt ope

1 iiii ii> not cbg2^ li^ A vncJT ! A X • . ^ A . / I

in ' 'X ^ fR-A o ^ K 7 . ^ -. :

Byn«/\^.^ X , - - - - - X i ^ . optnsetS. [X,,Y^^ . ( x ,L ^ 1 . -iy-'"> - - J r ^ J i J

clo&aA sets-. SML ^J'. ^ ^

I ^ _ [t^Jj^y ^ /v. _J^' , . - C ^ . T W cios^vt A of a ^ A-^. Av-..A U. \;vv»-*i cf A ^ ^ A U i p U ^

. . r y g f • ^w\ I D SIAOW A*^ dpevN 6=> A C A As IpAcA

: , ^ ' ^ ^ --^Vs^"- :

§6,1. COI tOjVVVV A •- - - • 'V / tW

U t X-^Y [(X,dxV(Y,div^) . Let X wi say - t W F .'s oa/rt:.at Xo t{ _ . -iWvt ey tst a K\b4 U ef Xo C t . r t u ^ c V ^

<=> If x-Y--v. cmi. \ ;f\^1

;:nV«A-.TFAE •. (fox- f: y-^v^ - . ^ . i l F is co\-t. a f X-Y -f is con. OS isl^

V\ f=or evev\ opev\V . f ^v) opcn.

j ^ P . . X-^Y. ^ - H v V h a . - R i ^ e V ^

r t

V is a nbc\f f(.x°") .bytjorct. asbUM(;i\d\. -c

a i^bc\ of Xo ^ . t . f (U^ CV- .Bwt X o e U c f ^ v ) ' ^

. So f"Yv) is o^<\ . - ,

W) » l e t Xo e X . \ € t V a of - f eXo' . Let - f^ '^V), by osS\Avyp\ht\ U 'fe ope*\

uH-^^^ i r t P ^ f

a .

U'Of.. X - ^ Y CO«fc.. " U Is coi^ . d s = ^ : g v i a

^ v ^ f . X ^ Y a - - Y ^ l -f'O^ - f ' / ^ is CWTt. ?^

l ^ ^ c x - 5 ^ , ^

! > ^ . i f ^cx ts 0. ^t^fc^i, »niLA^^ye^-ae>o, ncxx^ C A ^ ' .

doim-. 0 ejct (.AV- X \

\ \ >VTt A - X \_A'

ea A = A A

7 ^ .

A.