Section 22*: 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
Check the details of Example 3.
Considering all
subsets of
and their preimages,
,
,
,
and their union
should be open in
, while
,
and
should not be open (but they are closed).