Section 33: Problem 7 Solution
Working problems is a crucial part of learning mathematics. No one can learn topology merely by poring over the definitions, theorems, and examples that are worked out in the text. One must work part of it out for oneself. To provide that opportunity is the purpose of the exercises.
James R. Munkres
is a subspace of a compact Hausdorff space (§29, one-point compactification), which is normal (§32) and, hence, completely regular (§33, corollary from the Urysohn Lemma), therefore,
is completely regular (Theorem 33.2).