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A Regular Space on Which Every Real-Valued Function with a Closed Graph is Constant

Published online by Cambridge University Press:  20 November 2018

Ivan Baggs
Ivan Baggs*
Affiliation:
Department of Mathematics University of Alberta Edmonton, Alberta T6G 2G1 Canada
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Abstract

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An example is given of a regular space on which every real-valued function with a closed graph is constant. It was previously known that there are regular spaces on which every continuous function is constant. It is also shown here that there are regular spaces that support only constant real-valued continuous functions, but support non-constant real-valued functions with a closed graph.

Keywords

54C0554C1054C3054C50
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 4 , 01 December 1989 , pp. 417 - 424
Copyright
Copyright © Canadian Mathematical Society 1989

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