# Urysohn's lemma

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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

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#### 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. The expert examines Hausdorffiness lemmas.

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