Section 30: Problem 10 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
Fix any
. Consider all points that equals
at all but finitely many coordinates and equal some dense points at all others. There is a countable set of finite subsets of coordinates and for each a countable set of points we just defined.