P-spaces and the Whyburn property

• Autores: Angelo Bella, Camillo Costantini, Santi Spadaro
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 37, Nº 3, 2011, págs. 995-1015
• Idioma: inglés
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• Resumen

  • 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 (an assumption weaker than CH) implies the existence of a non-weakly Whyburn P-space of size aleph2. 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 Lindelof Whyburn P-spaces.