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When X* is a P′-Space

Published online by Cambridge University Press:  20 November 2018

Mary Anne Swardson  and
Paul J. Szeptycki
Mary Anne Swardson
Affiliation:
Department of Mathematics, 321 Morton Hall, Ohio University, Athens, OH, USA 45701, e-mail: swardson@oucsace.cs.ohiou.edu, szeptyck@oucsace.cs.ohiou.edu
Paul J. Szeptycki
Affiliation:
Department of Mathematics, 321 Morton Hall, Ohio University, Athens, OH, USA 45701, e-mail: swardson@oucsace.cs.ohiou.edu, szeptyck@oucsace.cs.ohiou.edu
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Abstract

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In [7,3.1 ] the authors show that if a space X is realcompact and locally compact, then X* is a P′-space. In this paper we show that the hypothesis of realcompactness can be weakened. We also look at other conditions on X that are sufficient to guarantee that X* is a P′-space.

Keywords

54D6054D3554D45P′-spaceorealcompactp-realcompactnearly realcompactlocally compacthyperisocompactstrongly isocompact(strongly) relatively pseudocompactwell separated
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 4 , 01 December 1996 , pp. 476 - 485
Copyright
Copyright © Canadian Mathematical Society 1996

References

1. Blair, R. L., Spaces in which special sets are z-embedded, Canad. J. Math. 28(1976), 673–690.Google Scholar
2. Blair, R. L. and van Douwen, E. K., Nearly realcompact spaces, Topology Appl. 47(1992), 209–221.Google Scholar
3. Blair, R. L. and Swardson, M. A., Spaces with an Oz Stone-Cech compactification, Topology Appl. 36( 1990), 73–92.Google Scholar
4. van Douwen, E. K., Remote points, Dissertationes Math. 188(1980), PWN, Warsaw.Google Scholar
5. Dykes, N., Mappings and realcompact spaces, Pacific J. Math. 31(1969), 347–358.Google Scholar
6. Blair, R. L., Generalizations of realcompact spaces, Pacific J. Math. 33(1970), 571—581.Google Scholar
7. Fine, N. J. and Gillman, L., Extension of continuous functions in ℕ, Bull. Amer. Math. Soc. 66(1960), 376–381.Google Scholar
8. Gillman, L. and Jerison, M., Rings of continuous functions, University Series in Higher Math., Van Nostrand, Princeton, 1960.Google Scholar
9. Hardy, K. and Woods, R. G., On c-realcompact spaces and locally bounded normal functions, Pac. J. Math. 43(1972), 647–656.Google Scholar
10. Mrowka, S., Some set-theoretic constructions in topology, Fund. Math. 94(1977), 83—92.Google Scholar
11. Schommer, J., Nearly realcompact and nearly pseudocompact spaces, PhD. dissertation, Ohio University, Athens.Google Scholar
12. Swardson, M. A., The character of certain closed sets, Canad. J. Math. 36(1984), 38–57.Google Scholar
13. Weir, M. D., Hewitt-Nachbin spaces, North Holland, Amsterdam, 1975.Google Scholar
14. Weiss, W., Countably compact spaces and Martin's axiom, Canad. J. Math. 30(1978), 243–249.Google Scholar