Section 32: Problem 1 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
Take two closed subset
in the closed subspace
.
and
are closed in
, therefore, they can be separated by disjoint neighborhoods
and
. Then
and
are disjoint neighborhoods of
and
in
.