From: "Dr. Michael Albert"
Subject: Re: Topology Question: Normal Spaces - stuck on a proof
Date: Wed, 1 Dec 1999 16:33:17 -0500
Newsgroups: sci.math
To: Martini
Remember that the following three statements are equivalent:
1) Given any two closed disjoint subsets C_1 and C_2, there
exists disjoint open subsets U_1 and U_2 such that
C_i is a subset of U_i for i=1,2.
2) Given any two closed disjoint subsets A and B, there is
a continous function which is equal to unity on A
and vanishes on B. (Urysohn's lemma).
3) Given any closed subset C and given any function f defined
on C and continuous (in the subspace topology), there is
a continuous extension F to the entire space. (Tietze's
extension theorm).
Hint: think about how you might inductively define a suitable
function.
Hope this isn't too late, but I hadn't had time to read this news
group in about a week.
By the way, is there any resourse on the web for getting the
pronunciations of names of mathematicians and scientists.
I'm really not sure how Tietze's name is pronounced.
Best wishes,
Mike