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    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

    © BrainMass Inc. brainmass.com March 4, 2021, 5:56 pm ad1c9bdddf
    https://brainmass.com/math/algebraic-geometry/urysohns-lemma-normal-spaces-19238

    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.

    $2.49

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