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

25 votes
3 answers
2k views

A rare property of Hausdorff spaces

Is there a Hausdorff topological space $X$ such that for any continuous map $f: X\longrightarrow \mathbb{R}$ and any $x\in \mathbb{R}$, the set $f^{-1}(x)$ is either empty or infinite?
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