2009/11/01 by Angelo Bella, Bella, Angelo, Camillo Costantini +3
Mathematics · #54A20 #54A35 #54B10 #54D20 #54G10 #FOS: Mathematics #General Topology (math.GN) #math.GN #msc:54A20 #msc:54A35 #msc:54B10 #msc:54D20 #msc:54G10
paper · pdf · doi:10.48550/arxiv.0911.0145
16 pages, to appear on the Houston Journal of Mathematics
arxiv created 2010/07/01 · arxiv updated 2010/07/02
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.