Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-18T13:00:20.754Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

References

1. Blumberg, H., New properties of all real functions, Trans. Amer. Math. Soc. 24 (1922), 113-128.Google Scholar
2. Husain, T., Almost continuous mappings, Prace Mat. 10 (1966), 1-7.Google Scholar
3. Kelley, John L., General Topology, D. Van Nostrand Co., Inc., Princeton, New Jersey, 1955.Google Scholar
4. Levine, Norman, A decomposition of continuity in topological spaces, Amer. Math. Monthly 68 (1961), 44-46.Google Scholar
5. Lin, Shwu-Yeng T. and Lin, Y.-F., On almost continuous mappings and Baire spaces, Canadian Mathematical Bulletin, Vol. 21, No. 2, pagesGoogle Scholar
6. Long, Paul E. and Herrington, Larry L., Properties of almost-continuous functions, Boll. Un. Mat. Ital. 10 (1974), 336-342.Google Scholar
7. Long, Paul E. and McGehee, Earl E. Jr., Properties of almost continuous functions, Proc. Amer. Math. Soc. 24 (1970), 175-180.Google Scholar
8. Noiri, Takashi, Between continuity and weak continuity, (Italian Summary) Boll. Un. Mat. Ital. 9 (1974), 647-654.Google Scholar
9. Noiri, Takashi, On weakly continuous mappings, Proc. Amer. Math. Soc. 46 (1974), 120-124.Google Scholar
10. Rose, David Alon, Weak continuity and almost continuity, Pacific Journal of Mathematics, to appear.Google Scholar
11. Singal, M. K. and Singal, Asha Rani, Almost-continuous mappings, Yokohama Math. Journal 16 (1968), 63-73.Google Scholar
12. Steen, Lynn A. and Arthur, Seebach Jr, Counterexamples in Topology, Holt, Rinehart and Winston, Inc., New York, 1970.Google Scholar