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Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
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Consistency of a strange (choice-wise) set of reals
The existence of such a set follows from $``\mathbb{R}$ is a countable union of countable sets.$"$ Let $\mathbb{R} = \bigcup_{n<\omega} S_n,$ each $S_n$ countable. Let $T_n = \{x \in \mathbb{R}: \exis …