Co-Blumberg spaces

Brown, J. B.; Piotrowski, Z.

doi:10.1090/S0002-9939-1986-0826502-4

Co-Blumberg spaces
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by J. B. Brown and Z. Piotrowski PDF

Proc. Amer. Math. Soc. 96 (1986), 683-688 Request permission

Abstract:

A pair $(X,Y)$ of topological spaces is said to be a Blumberg pair ("BP") if for every $f:X \to Y$, there exists a dense subset $D$ of $X$ such that $f|D$ is continuous. $X$ is a Blumberg space if $(X,R)$ is BP, where $R$ denotes the reals. $Y$ is co-Blumberg if $(R,Y)$ is BP. We survey the literature concerning the relationships between Blumberg spaces and Baire spaces and then study the relationships between co-Blumberg spaces and separability properties.

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