Do a Hausdorff space and its associated completely regular space have the same Borel subsets? – mathoverflow.net

Do a Hausdorff space and its associated completely regular space have the same Borel subsets? – mathoverflow.net

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Let $(X,T)$ be a Hausdorff topological space. Let $C_b(X)$ be its algebra of continuous bounded functions. Let $T'$ be the initial topology on $X$ given by $C_b(X)$. It is known that $T=T'$ if and ...

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