Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-24T05:38:35.700Z Has data issue: false hasContentIssue false
  • English
  • Français

Characterizations of a generalized notion of compactness

Published online by Cambridge University Press:  09 April 2009

George H. Butcher  and
James E. Joseph
George H. Butcher
Affiliation:
Department of Mathematics, Howard University, Washington, D. C.
James E. Joseph
Affiliation:
Department of Mathematics, Federal City College, Washington, D. C.
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 theorems which encompass known characterizations of many of the generalized compactness properties.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 22 , Issue 3 , November 1976 , pp. 380 - 382
Copyright
Copyright © Australian Mathematical Society 1976

References

Aleksandrov, P. and Urysohn, P. (1929), ‘Mémoire sur les espaces topologiques compacts’, Nederl. Akad. Wetensch Proc. Ser. A 14, 1–96.Google Scholar
Gál, I. S. (1957), ‘On a generalized notion of compactness, I’, Nederl. Akad. Wetensch Proc. Ser. A 60, 421–430.CrossRefGoogle Scholar
Gál, I. S. (1958), ‘On the theory of (m, n)-compact topological spaces’, Pacific J. Math. 8, 721–734.Google Scholar
Franklin, S. P. and Sorgenfrey, R. H. (1966), ‘Closed and image-closed relations’, Pacific J. Math. 19, 433–439.CrossRefGoogle Scholar
Hanai, S. (1961), ‘Inverse images of closed mappings, I’, Proc. Japan Acad. 37, 298–301.Google Scholar
Herrington, L. L. and Long, P. E. (1975), ‘Characterizations of H-closed spaces’, Proc. Amer. Math. Soc. 48, 469–475.Google Scholar
Hodel, R. E. and Vaughan, J. E. (1974), ‘A note on [a, b]-compactness’, Gen. Top. and Appl. 4, 179–189.Google Scholar
Joseph, J. (to appear), ‘On H-closed spaces’, Proc. Amer. Math Soc.Google Scholar
Joseph, J. (to appear), ‘Characterizations of nearly-compact spaces’, Boll. Un. Mat. Ital.Google Scholar
Joseph, J. (submitted for publication), ‘Characterizations of m-Lindelöf spaces’.Google Scholar
Kasahara, S. (1973), ‘Characterizations of compactness and countable compactness’, Proc. Japan Acad. 49, 523–524.Google Scholar
Mrowka, S. (1959), ‘Compactness and product spaces’, Colloq. Math. 7, 19–22.Google Scholar
Scarborough, C. T. (1969), ‘Closed graphs and closed projections’, Proc. Amer. Math. Soc. 20, 465–470.Google Scholar
Smirnov, Yu. M. (1950), ‘On topological spaces, compact in a given interval of powers’, Akad. Nauk. SSSR Izvest. Ser. Mat. 14, 155–178.Google Scholar
Vaughan, J. E. (1975), ‘Convergence, closed projections and compactness’, Proc. Amer. Math. Soc. 51, 469–475.Google Scholar
Vaughan, J. E. (1975), ‘Some properties related to [a, b]-compactness’, Fund. Math. 87, 251–260.CrossRefGoogle Scholar