/
a A of a space is at a A of a space is at

a A of a space is at - PDF document

ventuilog
ventuilog . @ventuilog
Follow
342 views
Uploaded On 2020-11-20

a A of a space is at - PPT Presentation

if closed which does not meet is at then a a a a a 1 a finite a any if and for finite a of exceeding with each a e V c U cV c U a a a of X n n a dimension a e X n ID: 819110

finite space union normal space finite normal union regular set covering sets hausdorff subset closed math totally meet open

Share:

Link:

Embed:

Download Presentation from below link

Download Pdf The PPT/PDF document "a A of a space is at" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.


Presentation Transcript

a A of a space is at if closed which do
a A of a space is at if closed which does not meet is at then a a a a a 1 a finite a any if and for finite a of exceeding

with each a e V c U cV c U = = a
with each a e V c U cV c U = = a a a of X = n = = n] a dimension a = e X, n = inductive dimensions, X X X = ^

^ X = X n = X = any of a ^ if and
^ X = X n = X = any of a ^ if and of p of p = U e V c U a any ^ if and covering of a any ^ e X = X n n X X X

W e n a e W F X cU X X X not X
W e n a e W F X cU X X X not X is a X e X p e W W. F c F c X, B F c X a a a X is a regular space, then norm

al space If every does not meet Q c V.
al space If every does not meet Q c V. = a a is and B and a a A is a set normal space = X—A. normal a finite totally n

ormal space e F cV cV cU; a union set
ormal space e F cV cV cU; a union sets closed X. If a \J an open a = a a \J F finite F F \J F set a set a AcU n

a normal space a a A is a n a a
a normal space a a A is a n a a paracompact normal space the union a union sets with each and each { a 0 n flj. +

e X e 0 , x e £ = U X is a normal
e X e 0 , x e £ = U X is a normal space, tlien e a a a = X is a totally normal space, then e X a a = \J of a ^

union of X, a normal space. X is par
union of X, a normal space. X is paracompact sets one tlie union sets, then set of X at is Bet X. X e = n, e U, X a ^

n F A = \J A X a a finite a a a X
n F A = \J A X a a finite a a a X a = ((Rxs a § 7 Y isan set space n X a a a normal space and n x a a X no

rmal space is union closed n e B of B,
rmal space is union closed n e B of B, X n B 6 n n regular / a X / 0 X is any there a regular space containing as an

subset such that If X space or normal s
subset such that If X space or normal space, so X*. X. A a (X*-l\) a L\ X = X X X W; U W X*-E, U X* e x A F F ^

0 A A V A A e A a A V A ^ UcW
0 A A V A A e A a A V A ^ UcW cWcV. W W X*— a X is a such that a regular space as an subset such� If X is a

normal is X*. X is a normal regular s
normal is X*. X is a normal regular space with has an subset that a A 4 n a (or T, j some T, T' S S ^ I be c c ^

e / / e a n a 0 finite covering {U
e / / e a n a 0 finite covering {U M a (open interval) of p in I and an ae T that, covering, cU,. c M a n) e (a,p)

n). a n a finite a V(j(p), n(p)), =
n). a n a finite a V(j(p), n(p)), = finite covering a special refinement. a n M c / 7 finite W(p a n a a finite a n a

a finite a finite finite a a / / a
a finite a finite finite a a / / a a the normal Hausdorff we have = = = e M if, JndM space finite a M is a i L\

; if c ^ a c W^) nMc = c U cV c U.
; if c ^ a c W^) nMc = c U cV c U. a n M * = A a e is a Hausdorff that a 0 = = = Q. a u Q anormal Hausdorff a

= y N a c N finite c 7 = F c V, F
= y N a c N finite c 7 = F c V, F = a a u a 2 is a Hausdorff 0 a = P = a c U a fi j ^ B ...U Bj. P a a P a

= = a S a = between those listed
= = a S a = between those listed all regular spaces. S Ctski la Fys. Theory Topology SSSR, URSS, Math. American Ma