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