Hostname: page-component-669899f699-7tmb6 Total loading time: 0 Render date: 2025-04-26T22:58:21.216Z Has data issue: false hasContentIssue false
  • English
  • Français

A metrisation theorem for pseudocompact spaces

Published online by Cambridge University Press:  17 April 2009

Chris Good  and
A. M. Mohamad
Chris Good
Affiliation:
School of Mathematics and Statistics, University of Birmingham, Birmingham, B15 2TT, United Kingdom, e-mail: [email protected]
A. M. Mohamad
Affiliation:
Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, Muscat, Oman, e-mail: [email protected]
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.

In this paper we prove that a completely regular pseudocompact space with a quasi-regular-Gδ-diagonal is metrisable.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 63 , Issue 1 , February 2001 , pp. 101 - 104
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Burke, D., ‘Covering properties’, in Handbook of Set-Theoretic Topology (North-Holland, Amsterdam, New York, 1984), pp. 347–422.CrossRefGoogle Scholar
[2]Gillman, L. and Jerison, M., Rings of continuous functions (Van Nostrand, Princeton, N.J., 1960).CrossRefGoogle Scholar
[3]Gartside, P.M. and Mohamad, A.M., ‘Cleavability of manifolds’, Topology Proc. 23 (1998), 151–166.Google Scholar
[4]Hewitt, E., ‘Rings of real–valued continuous functions. I’, Trans. Amer. Math. Soc. 64 (1948), 45–99.CrossRefGoogle Scholar
[5]Lee, K., ‘Spaces in which compacta are uniformly regular G δ’, Pacific J. Math. 81 (1979), 435–445.CrossRefGoogle Scholar
[6]McArthur, W., ‘G δ–diagonals and metrization theorems’, Pacific J. Math. 44 (1973), 613–617.CrossRefGoogle Scholar
[7]Shiraki, H., ‘A note on spaces with a uniform base’, Proc. Japan. Acad. Ser. A Math. Sci 47 (1971), 1036–1041.CrossRefGoogle Scholar