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On Levine′s Decomposition of Continuity

Published online by Cambridge University Press:  20 November 2018

David Alon Rose
David Alon Rose*
Affiliation:
Division of Science and Mathematics, University of Tampa, Tampa, Florida 33606
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Abstract

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A strong version of Levine′s decomposition of continuity leads to the result that a closed graph weakly continuous function into a rim-compact space is continuous. This result implies a closed graph theorem: every almost continuous closed graph function into a strongly locally compact space is continuous. An open problem of Shwu-Yeng T. Lin and Y.-F. Lin asks if every almost continuous closed graph function from a Baire space to a second countable space is necessarily continuous. This question is answered in the negative by an example.

Keywords

54C1054C0554D45
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 21 , Issue 4 , 01 December 1978 , pp. 477 - 481
Copyright
Copyright © Canadian Mathematical Society 1978

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