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On subspaces of pseudo-radial spaces

Jin Yuan Zhou (1993)

Commentationes Mathematicae Universitatis Carolinae

It is proved that, under the Martin’s Axiom, every T 1 -space with countable tightness is a subspace of some pseudo-radial space. We also give several characterizations of subspaces of pseudo-radial spaces and conclude that being a subspace of a pseudo-radial space is a local property.

On the Hausdorff Dimension of Topological Subspaces

Tomasz Szarek, Maciej Ślęczka (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

It is shown that every Polish space X with d i m T X d admits a compact subspace Y such that d i m H Y d where d i m T and d i m H denote the topological and Hausdorff dimensions, respectively.

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