Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-25T04:03:49.579Z Has data issue: false hasContentIssue false
  • English
  • Français

Characterizations of functionally compact spaces

Part of: Fairly general properties

Published online by Cambridge University Press:  09 April 2009

L. L. Herrington
L. L. Herrington
Affiliation:
Department of Mathematics University of Arkansas at Pine BluffPine Bluff, Arkansas 71601, U.S.A.
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.

This paper gives characterizations of functionally compact spaces in terms of filterbases and nets. Also, a topological property that is weaker than countable compactness but stronger than first countable minimality is investigated.

MSC classification

Secondary: 54D20: Noncompact covering properties (paracompact, Lindelöf, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 29 , Issue 1 , February 1980 , pp. 71 - 79
Copyright
Copyright © Australian Mathematical Society 1980

References

Dickman, R. F. Jr and Zame, A. (1969), ‘Functionally compact spaces’, Pacific J. Math. 31, 303–311.Google Scholar
Gross, G. and Viglino, G. (1970), ‘Some topological properties weaker than compactness’, Pacific J. Math. 35, 635–638.Google Scholar
Herrington, L. L. and Long, P. E. (1975a), ‘Characterizations of C-compact spaces’, Proc. Amer. Math. Soc. 52, 417–426.Google Scholar
Herrington, L. L. and Long, P. E. (1975b), ‘Characterizations of H-closed spaces’, Proc. Amer. Math. Soc. 48, 469–475.Google Scholar
Kasahara, S. (1973), ‘Characterizations of compactness and countable compactness’, Proc. Japan Acad. 49, 523–524.Google Scholar
Levine, N. (1961), ‘A decomposition of continuity in topological spaces’, Amer. Math. Monthly 68, 44–46.Google Scholar
Lim, Teck-Cheong and Tan, Kok-Keong (1974), ‘Functionally compactness and C-compactness’, J. London Math. Soc. (2), 9, 317–377.Google Scholar
Stephenson, R. M. Jr (1969), ‘Minimal first countable topologies’, Trans. Amer. Math. Soc., 138, 115–127.CrossRefGoogle Scholar
Velicko, N. V. (1969), ‘H-closed topological spaces’, English transl., Amer. Math. Soc. Transl. 78 (2), 103–118.Google Scholar