On thick spaces
On thin-tall scattered spaces
On tightness in chain-net spaces
On topological and algebraic structure of extremally disconnected semitopological groups
Starting with a very simple proof of Frol’ık’s theorem on homeomorphisms of extremally disconnected spaces, we show how this theorem implies a well known result of Malychin: that every extremally disconnected topological group contains an open and closed subgroup, consisting of elements of order . We also apply Frol’ık’s theorem to obtain some further theorems on the structure of extremally disconnected topological groups and of semitopological groups with continuous inverse. In particular, every...
On van Douwen spaces and retracts of
Eric van Douwen produced in 1993 a maximal crowded extremally disconnected regular space and showed that its Stone-Čech compactification is an at most two-to-one image of . We prove that there are non-homeomorphic such images. We also develop some related properties of spaces which are absolute retracts of expanding on earlier work of Balcar and Błaszczyk (1990) and Simon (1987).
On κ-Lindelöf spaces
We use the Hausdorff pseudocharacter to bound the cardinality and the Lindelöf degree of κ-Lindelöf Hausdorff spaces.
On -caliber and an application of Prikry’s partial order
We study the concept of -caliber as an alternative to the well known concept of caliber. -caliber and caliber values coincide for regular cardinals greater than or equal to the Souslin number of a space. Unlike caliber, -caliber may take on values below the Souslin number of a space. Under Martin’s axiom, is a -caliber of . Prikry’s poset is used to settle a problem by Fedeli regarding possible values of very weak caliber.
One folkloristic lemma on cardinal reflections in Unif
Open and proper maps between convergence spaces