1. ## countable+discrete=separable?

Is every countable discrete set - separable? If yes, why? Thank you.

2. Hi

In such case, isn't the set itself a countable dense subset?

3. Originally Posted by georgel
Is every countable discrete set - separable? If yes, why? Thank you.

Well yes, and in a rather trivial way: as every singleton is open, there exists a countable set of points (all the points of the space!) s.t. every open subset of the space contains at least one of these points...

Tonio