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Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
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A compact T1 topological space has a proper dense subset to which it is homeomorphic. What c...
Let $X$ be a compact T1 (so singleton subsets are closed) topological space. Suppose that there is a proper subset $D \subset X$ such that:
$D$ is dense in $X$;
$D$ is homeomorphic to $X$.
Note th …