Section 32: Problem 3 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

Theorem 29.2: If

is Hausdorff then it is locally compact iff for every

and its neighborhood

there is its neighborhood

such that

is compact. Lemma 31.1: If

then it is regular iff for every

and its neighborhood

there is its neighborhood

such that

. Therefore, if

is Hausdorff and locally compact then it is

and regular.

Subpages

Section 32: Problem 3 Solution

Section 32: Problem 3 Solution