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