Section 31: 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
Show that if
is regular, every pair of points of
have neighborhoods whose closures are disjoint.
For
and
take first a neighborhood
of
such that
, and then a neighborhood
of
such that
.