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Almost Continuity of Mappings

Published online by Cambridge University Press:  20 November 2018

Shwu-Yeng T. Lin
Shwu-Yeng T. Lin*
Affiliation:
University of South Florida
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Let E be a metric Baire space and f a real valued function on E. Then the set of points of almost continuity in E is dense (everywhere) in E.

Our purpose is to set this result in its most natural context, relax some very restricted hypotheses, and to supply a direct proof. More precisely, we shall prove that the metrizability of E in Theorem H may be removed, and that the range space may be generalized from the (Euclidean) space of real numbers to any topological space satisfying the second axiom of countability [2].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 3 , August 1968 , pp. 453 - 455
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Husain, T., Almost continuous mapping. Prace Matematyczne 10 (1966) 1-7.Google Scholar
2. Kelley, J. L., General topology. Van Nostrand, Princeton, 1955.Google Scholar
3. Moore, R. L., Foundations of point set theory. Amer. Math. Soc. Colloquium Publications, Vol. 13(1932, rev. ed., 1962).Google Scholar