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pointwise self-homeomorphic

A topological space X is called pointwise self-homeomorphic at a point $x \in X$ if for any neighborhood U of x there is a set V such that $x\in V \subseteq U$ and V is homeomorphic to X. The space X is called pointwise self-homeomorphic if it is pointwise self-homeomorphic at each of its points.

Janusz J. Charatonik, Pawel Krupski and Pavel Pyrih
2001-02-21