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On Almost Continuous Mappings and Baire Spaces

Published online by Cambridge University Press:  20 November 2018

Shwu-Yeng T. Lin  and
You-Feng Lin
Shwu-Yeng T. Lin
Affiliation:
Department of Mathematics, University of South Florida, Tampa, Florida 33620, USA
You-Feng Lin
Affiliation:
Department of Mathematics, University of South Florida, Tampa, Florida 33620, USA
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Abstract

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It is proved, in particular, that a topological space X is a Baire space if and only if every real valued function f: X →R is almost continuous on a dense subset of X. In fact, in the above characterization of a Baire space, the range space R of real numbers may be generalized to any second countable, Hausdorfï space that contains infinitely many points.

Keywords

54C1054F6554D1054D15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 21 , Issue 2 , 01 June 1978 , pp. 183 - 186
Copyright
Copyright © Canadian Mathematical Society 1978

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