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).
In this paper we introduce two classes of functions called weakly preopen and weakly preclosed functions as generalization of weak openness and weak closedness due to [26] and [27] respectively. We obtain their characterizations, their basic properties and their relationshisps with other types of functions between topological spaces.
Weakly bisequential spaces were introduced by A.V. Arhangel'skii [1], in this paper. We discuss the relations between weakly bisequential spaces and metric spaces, countably bisequential spaces, Fréchet-Urysohn spaces.
We use the Hausdorff pseudocharacter to bound the cardinality and the Lindelöf degree of κ-Lindelöf Hausdorff spaces.
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.
We continue the study of almost--resolvable spaces beginning in A. Tamariz-Mascar’ua, H. Villegas-Rodr’ıguez, Spaces of continuous functions, box products and almost--resoluble spaces, Comment. Math. Univ. Carolin. 43 (2002), no. 4, 687–705. We prove in ZFC: (1) every crowded space with countable tightness and every space with -weight is hereditarily almost--resolvable, (2) every crowded paracompact space which is the closed preimage of a crowded Fréchet space in such a way that the...
We show that a (weakly) Whyburn space may be mapped continuously via an open map onto a non (weakly) Whyburn space . This fact may happen even between topological groups and , a homomorphism, Whyburn and not even weakly Whyburn.