Abstract:
n this report, some properties ofthe separation ofany two distinct points, points and closed sets,
and any two closed sets in a topological space are studied. Particularly, we can separate any two
closed sets on a normal space by a continuous function.
Urysohn was able to associate a continuous function
f: X ~ [a, b]which separates the subsets A
and B ofa normal space X; in the sense that f maps A to a, and B to b and also it asserts the
existence
ofcertain real-valued continuous functions on a normal space X