Theorem 5.5. If X and Y are separable spaces, then X X Y is separable. Definition. Let A be a subset of a topological space X. Then A is dense in X if and only if A = X. Definition. A topological space X is separable if and only if X has a countable dense subset.

Theorem 5.5. If X and Y are separable spaces, then X X Y is separable.
Definition. Let A be a subset of a topological space X. Then A is dense in X if and only
if A = X.
Definition. A topological space X is separable if and only if X has a countable dense
subset.

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