Proof of Converse of Urysohn's Lemma
If a topological spaceis normal then, given any disjoint non empty closed subsetsandofthere is a continuous functionwherehas the absolute value topology, such that for everyand for every
Proof That the Converse of Urysohn's Lemma is true
Supposehas the property described in Urysohn's Lemma. Letandbe non empty closed subsets ofThere is a continuous functionsuch that for all
The setsandare disjoint open sets subsets ofSinceis continuousandare disjoint open subsets ofsuch thatandhenceis normal.