Section 33: 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
(a) Follows from (b), but, in fact, we will prove (b) based on (a). For any completely separable space: take two points, a continuous function that separates them, if some point
in the image is missing, can separate:
and
.(b) Countable regular implies countable Lindelöf regular implies countable normal. By (a), if it has at least two points, it is disconnected.