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On Approximately Continuous and Almost Continuous Functions

Published online by Cambridge University Press:  20 November 2018

M. Chaika  and
S. Perlman
M. Chaika
Affiliation:
Syracuse University, Syracuse, New York
S. Perlman
Affiliation:
Syracuse University, Syracuse, New York
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The purpose of this note is to discuss the relationship between the concepts of approximate continuity and almost continuity of real functions of a real variable.

Contrary to the papers of T. Husain [1], [2], [3], we shall show that there is little relationship between these concepts, that approximate continuity does not imply almost continuity without additional restrictions and we shall give one such restriction.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 3 , September 1971 , pp. 433 - 435
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Husain, T., B(T)-Spaces and the closed graph theorem, Math. Ann. 153 (1964), 293-298.Google Scholar
2. Husain, T. and Dwivedi, T. D., A characterization of real almost continuous functions, Canad. Math. Bull. (3) 10 (1967), 361-364.Google Scholar
3. Husain, T., Some remarks about real almost-continuous functions, Math. Mag. (5) 40 (1967). 250-254.Google Scholar
4. Goffman, C., Real functions, Holt, New York, 1953.Google Scholar
5. Saks, S., Theory of the integral, Dover, New York, 1964.Google Scholar