Section 30: Problem 3 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
Suppose the number of limit points in
is countable. For each point in
that is not a limit point take a basis neighborhood that contains this point in
only. All such neighborhoods must be different. Contradiction.