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3. E.K. van Douwen The Integers and Topology in Handbook of Set-theoretic Topology (K.Kunen

By Angelo (i-catn) Simon

Abstract

Pseudocompact Whyburn spaces of countable tightness need not be Fréchet. (English summary) Proceedings of the 20th Summer Conference on Topology and its Applications. Topology Proc. 30 (2006), no. 2, 423–430. A Hausdorff space X is said to be Whyburn if for each set A ⊆ X and x ∈ cl(A) � A there is some B ⊆ A such that cl(B) � A = {x}. It was shown by V. V. Tkachuk and I. V. Yashchenko [Comment. Math. Univ. Carolin. 42 (2001), no. 2, 395–405; MR1832158 (2002b:54004)] that every countably compact regular Whyburn space is Fréchet, and in the same paper they asked if a similar result holds for pseudocompact Whyburn spaces. In [Proc. Amer. Math. Soc. 131 (2003), no. 10, 3257–3265 (electronic); MR1992867 (2004g:54005)], J. Pelant, M. G. Tkachenko, Tkachuk and the reviewer gave a ZFC example of a pseudocompact (Tikhonov) Whyburn space of uncountable tightness (and hence which is not Fréchet). In the paper under review, assuming the continuum hypothesis, the authors construct a pseudocompact Whyburn space of countable tightness which is not Fréchet. Reviewed by Richard Wilso

Year: 2013
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