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A note on pseudocompact spaces

Part of: Maps and general types of spaces defined by maps Fairly general properties

Published online by Cambridge University Press:  09 April 2009

James E. Joseph
James E. Joseph
Affiliation:
Department of Mathematics Howard University Washington, D.C. 20059, U.S.A.
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Abstract

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In this note we give several new characterizations of arbitrary pseudocompact spaces, that is spaces characterized by the property that all continuous real-valued functions on the space are bounded.

Keywords

pseudocompactnessfilterbasescomplete accumulation points.

MSC classification

Secondary: 54D20: Noncompact covering properties (paracompact, Lindelöf, etc.) 54C30: Real-valued functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 27 , Issue 4 , June 1979 , pp. 408 - 410
Copyright
Copyright © Australian Mathematical Society 1979

References

Bagley, R. W., Connell, E. H. and McKnight, J. D. Jr, (1958), ‘On properties characterizing pseudocompact spaces’, Proc. Amer. Math. Soc. 9, 500–506.CrossRefGoogle Scholar
Comfort, W. W. (1967), ‘A nonpseudocompact product space whose finite subproducts are pseudocompact’, Math. Ann. 170, 41–44.CrossRefGoogle Scholar
Frolik, Z. (1960), ‘The topological products of two pseudo compact spaces’, Czechoslovak Math. J. 10, 339–349.CrossRefGoogle Scholar
Gillman, L. and Jerison, M. (1960), Rings of Continuous Functions (Van Nostrand, New York).CrossRefGoogle Scholar
Glicksberg, I. (1952), ‘The representation of functionals by integrals’, Duke Math J. 19, 253–261.CrossRefGoogle Scholar
Glicksberg, I. (1959), ‘Stone Ĉech compactifications of products’, Trans. Amer. Math. Soc. 90, 369–382.Google Scholar
Herrington, L. L. and Long, P. E. (1975), ‘Characterizations of C-compact spaces’, Proc. Amer. Math. Soc. 52, 417–426.Google Scholar
Hewitt, E. (1948), ‘Rings of real-valued continuous functions’, Trans. Amer. Math. Soc. 64, 45–99.Google Scholar
Joseph, J. E. (1977), ‘More characterizations of H-closed spaces’, Proc. Amer. Math. Soc. 63, 160–164.Google Scholar
Joseph, J. E. (1978), ‘Pseudocompactness and closed subsets of products’, Proc. Amer. Math. Soc. (to appear).CrossRefGoogle Scholar
Kelley, J. L. (1955), General Topology Van Nostrand, Princeton.Google Scholar
Stephenson, R. M. Jr, (1968), ‘Pseudocompact spaces’, Trans. Amer. Math. Soc. 134, 437–448.CrossRefGoogle Scholar