Explore BrainMass

Urysohn's lemma

A Hausdorff space is said to be completely regular if
for each pt. x in X and closed set C with x not in C,
there exists a continuous function f: X --> {0,1} s.t.
f(x)=0 and f(C)={1}.

Show that if a space is normal, it is completely regular.
How do I use Urysohn's lemma along with Hausdorffiness to show this.

Thank You

Solution Preview

Urysohn's Lemma: The topological space X satisfies T4 axiom if and only if for any nonintersected closed set A and B, there exists a continuous function f: X->[0,1], such that f(A)={0}, ...

Solution Summary

This is a proof regarding regular and normal spaces.