Tightness, character and related properties of hyperspace topologies
type: Item
instance of: scholarly article
title: Tightness, character and related properties of hyperspace topologies
zbMATH Open document ID: 1065.54003
author: Camillo Costantini
author: Paolo Vitolo
author: Ľubica Holá
published in: Topology and its Applications
publication date: 2004-11-23T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 54B20
Mathematics Subject Classification ID: 54A25
Mathematics Subject Classification ID: 54D55
Mathematics Subject Classification ID: 54A20
Mathematics Subject Classification ID: 54E35
zbMATH DE Number: 2117957
zbMATH Keywords: hyperspace
zbMATH Keywords: cardinality properties. sequential space
zbMATH Keywords: convergence
zbMATH Keywords: metric space
reviewed by: Aleksandr A. Ivanov
MaRDI profile type: Publication
full work available at URL: j.topol.2004.02.007
OpenAlex ID: W2011836551
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DOI: 10.1016/J.TOPOL.2004.02.007
description: scientific article; zbMATH DE number 2117957