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.
A. Bella, C. Costantini, & S. Spadaro (2011). P-spaces and the Whyburn Property. HOUSTON JOURNAL OF MATHEMATICS, 37(3), 995-1015.
Data di pubblicazione: | 2011 | |
Titolo: | P-spaces and the Whyburn Property | |
Autori: | ||
Citazione: | A. Bella, C. Costantini, & S. Spadaro (2011). P-spaces and the Whyburn Property. HOUSTON JOURNAL OF MATHEMATICS, 37(3), 995-1015. | |
Rivista: | ||
Settore Scientifico Disciplinare: | Settore MAT/03 - Geometria | |
Appare nelle tipologie: | 1.01 Articolo in rivista |
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