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Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
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Is a cofinite topology for a set with cardinality between $\aleph_{0}$ and $2^{\aleph_{0}}$ ...
It is easy to show that $\mathbb{N}$ with the cofinite topology is not path connected and that any set with cardinality $\geq 2^{\aleph_0}$ equipped with the cofinite topology is in fact path connec …