[Math] Every metric space with a countable base is separable

general-topologymetric-spaces

I know that every separable metric space has a countable base.

I was wondering if we can get a countable dense subset from every metric space that has a countable base.

Thank you very much!!

Best Answer

You don't even need a metric space for that direction, in holds in general. If your topology has a countable base, just pick one element out of every base set and you will get a countable dense subset.

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