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A Characterization of Real almost Continuous Functions

Published online by Cambridge University Press:  20 November 2018

T. Husain  and
T. D. Dwivedi
T. Husain
Affiliation:
McMaster University Sir George Williams University
T. D. Dwivedi
Affiliation:
McMaster University Sir George Williams University
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The main purpose of this note is to give a characterization of almost continuous functions similar to that of approximately continuous functions ([3], §235, p. 312). The characterization of approximately continuous real functions has been used to show that each approximately continuous function is almost continuous ([4], §6). Thus combining these results we see that the classes of almost continuous, approximately continuous and continuous functions form a descending chain.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 3 , August 1967 , pp. 361 - 364
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Dwivedi, T. D., A characterization theorem for almost continuous functions. Master′ s Thesis, University of Ottawa.Google Scholar
2. Goffman, C., Real Functions. Reinhart and Company, Inc. 1953.Google Scholar
3. Hobson, E. W., The Theory of Functions of a Real Variable. Vol. I. Dover, New York, 1957.Google Scholar
4. Husain, T., B(T)-Spaces and the Closed Graph Theorem. Math. Ann. 153 (1966), 293-298 Google Scholar