Is there a separable and metrisable topological space $X$ so that $ \operatorname{card}(X) > {2}^{\aleph_{0} }$?
I can't think of an example.
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1Possible duplicate of Cardinality of separable metric spaces. Or Every separable metric space has cardinality less than or equal to the cardinality of the continuum. – YuiTo Cheng Apr 22 '19 at 11:14
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Hint: any point of $X$ is a limit of a sequence from the countable dense subset. How many such sequences are there? – Wojowu Apr 22 '19 at 11:15