A Regular Space on Which Every Real-Valued Function with a Closed Graph is Constant
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Published:1989-12-01
Issue:4
Volume:32
Page:417-424
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ISSN:0008-4395
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Container-title:Canadian Mathematical Bulletin
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language:en
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Short-container-title:Can. math. bull.
Abstract
AbstractAn 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.
Publisher
Canadian Mathematical Society
Subject
General Mathematics
Cited by
1 articles.
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1. P-spaces and an unconditional closed graph theorem;Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas;2010-03