Section 30: Problem 2 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 us choose
as in the hint (whenever it is possible). It is a countable subcollection of
which is a basis: for any open
and
there is an open set
containing
, an open set
containing
and an open set
containing
, thus,
does exist.