Section 30: Problem 5 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) For each point in the dense take a countable collection of balls of radius
centered at the point. Let
,
is open. There is a ball
. Find a dense point
in
where
. Then
.(b) Similar to exercise 4 (the first part) with the only difference that the subcovering is going to be countable.