91Ó°ÊÓ

Prove that if \(M\) is an uncountable subset of a topological space with a countable base, then some point of \(M\) is a limit point of \(M\).

Prove that a topological space satisfying the second axiom of countability automatically satisfies the first axiom of countability.

Give an example of a topological space satisfying the first axiom of countability but not the second axiom of countability.