Urysohn's Lemma by Benjamin Bui '19, Wednesday, December 5, 2018, 1 - 1:45 pm, Stetson Court Classroom 101, Mathematics Colloquium

Urysohn’s Lemma by Benjamin Bui ’19, Wednesday, December 5, 2018, 1 – 1:45 pm, Stetson Court Classroom 101, Mathematics Colloquium

Abstract:  Pavel S. Urysohn developed his eponymous lemma which actually proved to be a fundamental result in the field of Topology when discussing normal spaces.  Although this lemma was originally used to prove Urysohn’s metrization theorem, its use has extended far beyond that singular application.  The lemma itself proves that there exists a continuous function f from a normal space, X, to an arbitrary closed subset, [a,b], of R such that, given two closed, disjoint subsets A and B, f(a’)=a and f(b’)=b for all a’ in A and b’ in B.