Urysohn's lemma
Not what you're looking for? Search our solutions OR ask your own Custom question.
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 May 24, 2023, 1:22 pm ad1c9bdddfhttps://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