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Proceedings of the American Mathematical Society

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

 

 

Conditions implying continuity of open and closed functions


Author: Ivan Baggs
Journal: Proc. Amer. Math. Soc. 33 (1972), 185-190
MSC: Primary 54C10
DOI: https://doi.org/10.1090/S0002-9939-1972-0292041-5
MathSciNet review: 0292041
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Abstract: It is shown that every open and closed real valued function of a real variable is continuous. This result is then extended to the case where the domain space is first countable and regular for a special class of open and closed functions.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0292041-5
Keywords: Open functions, closed functions, peripherally continuous functions, continuous functions, first countable regular spaces
Article copyright: © Copyright 1972 American Mathematical Society