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- #1

- Feb 29, 2012

- 342

Let $f: X \to Y$ be continuous. Show that if X is Lindelöf, or if X has a countable dense subset, then $f(X)$ satisfies the same condition.

I don't know how to work with the Lindelöf condition. I've done the countable dense subset, though:

Just for reference, I know the definition of Lindelöf but I am having trouble proving things with it. Here it is:

Thanks!

Regards.