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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 question on cofinite topology.

Let $X$ be a countably infinite (or larger) set with the cofinite topology. for every $x\in X$ is there exists a family $\xi\subset\tau$ such that $\lbrace x\rbrace=\bigcap\xi $ ? If the answer is yes …
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