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Extra Countably Compact Spaces

Published online by Cambridge University Press:  20 November 2018

Victor Saks
Victor Saks*
Affiliation:
Daemen College, Amherst New York 14226
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Abstract

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A completely regular HausdorfT space is extra countably compact if every infinite subset of βX has an accumulation point in X. It is a theorem of Comfort and Waiveris that if X either an F-space or realcompact (topologically complete), then there is a set {Pξ:ξ<2C} of extra countably compact (countably compact) subspaces of αX such that Pξ ∩ Pξ = X, for ξ<ξ'<2C. Comfort and Waiveris conjecture that in all three cases, the spaces may be chosen pairwise non-homeomorphic. We prove this conjecture, using D- limits and weak P-points. We also give a partial solution to another question asked by Comfort and Waiveris.

Keywords

54D3054D3554A25Key words and phrasesExtra countably compacthomeomorphicD-limitsweak P-pointscountably compact

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 4 , 01 December 1983 , pp. 473 - 481
Copyright
Copyright © Canadian Mathematical Society 1983

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