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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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