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Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.

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Does there exist a topology for a set X which is compact and Hausdorff? [closed]

For every set $X$ and every topology $\tau$ over $X$ we have that $\tau$ contains the trivial topology $\{ X, \emptyset\}$, which is compact, and is contained in the discrete topology $\{ S: S \subset …
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