Section 29: Problem 4 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
Suppose
where
is open and
is compact, then there are two balls centered at
such that
. But then
as a closed subset of compact set must be compact, but it is not (similar to Exercise 1 of the previous section).