P-spaces and the Whyburn Property

Santi Domenico Spadaro, Santi Spadaro, Angelo Bella, Camillo Costantini

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3 Citazioni (Scopus)

Abstract

We investigate the Whyburn and weakly Whyburn property in the class of P-spaces, that is spaces where every countable intersection of open sets is open. We construct examples of non-weakly Whyburn P-spaces of size continuum, thus giving a negative answer under CH to a question of Pelant, Tkachenko, Tkachuk and Wilson. In addition, we show that the weak Kurepa Hypothesis (a set-theoretic assumption weaker than CH) implies the existence of a non-weakly Whyburn P-space of size ℵ2. Finally, we consider the behavior of the above-mentioned properties under products; we show in particular that the product of a Lindelöf weakly Whyburn P-space and a Lindelöf Whyburn P-space is weakly Whyburn, and we give a consistent example of a non-Whyburn product of two Lindelöf Whyburn P-spaces.
Lingua originaleEnglish
pagine (da-a)995-1015
Numero di pagine21
RivistaHouston Journal of Mathematics
Volume37
Stato di pubblicazionePublished - 2011

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