Extra Countably Compact Spaces

Saks, Victor

Canadian mathematical bulletin, Tome 26 (1983) no. 4, pp. 473-481

Résumé

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.

Détail

DOI : 10.4153/CMB-1983-076-0

Mots-clés : 54D30, 54D35, 54A25, Key words and phrases, Extra countably compact, homeomorphic, D-limits, weak P-points, countably compact

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