It is well-known (1, 2) that the cardinality of a separable Hausdorff topological space is at most $2^{2^{\aleph_0}}$. Therefore, the collection $\mathcal{A}$ of all (homeomorphism classes of) separable Hausdorff topological spaces is a set. Can the set $\mathcal{A}$ be equipped with a natural topology?
2026-03-20 04:03:33.1773979413
Topology on the set of all separable Hausdorff topological spaces
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