Tightness, character and related properties of hyperspace topologies
The paper consists of an introduction and six sections. The introduction is a short review of the authors' new results on cardinality properties of hyperspaces with (upper or lower) Fell and Vietoris topologies and some corresponding known results. The first section (preliminaries) contains some definitions and statements on topological spaces and cardinal functions which are needed for the subsequent sections. In the second section (tightness and character) the authors investigate the tightness and the character of hyperspaces with the topologies \(V^{-}\), C and F. The following sections (third: sequentiality, sequential order; fourth: Fréchet property; fifth: pseudoradiality and radiality) contain accordingly propositions on sequentiality, Fréchet property, pseudoradiality and radiality of hyperspaces endowed with the above-mentioned topologies. The sixth section (counterexamples) contains six examples of (countable, hereditarily paracompact) spaces having special cardinality properties. In the last one the authors construct countably tight spaces \((X,\sigma)\) and \((X,\tau)\) such that \((X,\sigma\vee\tau)\) is not countably tight.
cardinality properties. sequential space
scientific article; zbMATH DE number 2117957
scientific article