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Almost Continuous Functions with Closed Graphs

Published online by Cambridge University Press:  20 November 2018

Andrew J. Berner
Andrew J. Berner*
Affiliation:
Department of Mathematics, University of Dallas, Irving Texas 75061, U.S.A.
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Abstract

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A function f:X → Y is almost continuous if for every x ∊ X and for each open set V ⊂ Y containing f(x), Cl(f-l(V)) is a neighborhood of x. Various conditions are given that guarantee that an almost continuous function is continuous. The main theorem states that if f:X → Y is almost continuous with a closed graph (closed in X × Y) and X and Y are complete metric spaces, then f is continuous.

Keywords

54C0854E50almost continuous functioncomplete metric space

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 25 , Issue 4 , 01 December 1982, pp. 428 - 434
Copyright
Copyright © Canadian Mathematical Society 1982

References

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