Section 26: 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
Let
be closed in
and suppose
. Suppose
then
and, since
is closed,
is open and contains a slice
. By the tube lemma there is also a tube about the slice that does not intersect
. Its projection is an open neighborhood of
that does not intersect
.