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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Universally first return continuous functions


Authors: Udayan B. Darji, Michael J. Evans and Richard J. O’Malley
Journal: Proc. Amer. Math. Soc. 123 (1995), 2677-2685
MSC: Primary 26A21; Secondary 26A15, 26A24
MathSciNet review: 1233966
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Abstract: It is known that the first return continuous functions are precisely the Darboux functions in Baire class 1, and that every such function can be changed via a homeomorphism into an approximately continuous function. Here we give two characterizations of the smaller class of universally first return continuous functions, one of which is the capacity of changing such a function via a homeomorphism into an approximately continuous function which is continuous almost everywhere.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1233966-9
PII: S 0002-9939(1995)1233966-9
Keywords: First return continuity, approximate continuity, a.e. topology, Baire class one, Darboux
Article copyright: © Copyright 1995 American Mathematical Society