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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Co-Blumberg spaces

Authors: J. B. Brown and Z. Piotrowski
Journal: Proc. Amer. Math. Soc. 96 (1986), 683-688
MSC: Primary 54C30; Secondary 26A03
MathSciNet review: 826502
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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\vert 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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Keywords: Blumberg's theorem, Baire space, separability
Article copyright: © Copyright 1986 American Mathematical Society