Let $X,Y$ be two homeomorphic topological spaces and let $d(X)$ denote the minimal cardinality of a subset $A \subseteq X$ such that $\bar A=X$, i.e., $A$ is dense in $X$. Then is it true that $d(X)=d(Y)$ when $X,Y$ are homeomorphic? I would appreciate even a proof for metric spaces $X,Y$. Thanks in advance
2026-04-02 23:59:26.1775174366
Do homeomorphic metric spaces have equal minimal cardinality of dense subsets?
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Hints in case of homeomorphism image of a dense set is dense. And remember homemomorphism means it is a bijective map.