Extraresolvability and cardinal arithmetic
type: Item
instance of: scholarly article
zbMATH Open document ID: 0976.54004
publication date: 2001-12-17T00:00:00Z
full work available at URL: https://eudml.org/doc/121453
Mathematics Subject Classification ID: 54A25
Mathematics Subject Classification ID: 54F99
Mathematics Subject Classification ID: 54A35
Mathematics Subject Classification ID: 03E35
zbMATH DE Number: 1682890
zbMATH Keywords: extraresolvability
zbMATH Keywords: product
zbMATH Keywords: topological group
author: Ofelia T. Alas
author: Salvador Garcia-Ferreira
author: Artur Hideyuki Tomita
MaRDI profile type: Publication
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title: Extraresolvability and cardinal arithmetic
published in: Commentationes Mathematicae Universitatis Carolinae
review text: A Tikhonov space \(X\) without isolated points is said to be extraresolvable (by Malykhin) if it contains a system \(\mathcal D\) of dense subsets such that two members of \(\mathcal D\) intersect in a nowhere dense set and \(|{\mathcal D}|\) is bigger than the least cardinality \(\Delta X\) of a nonempty open subset of \(X\). Extraresolvability of certain products and of generalized \(\Sigma \)-products depend on cardinal arithmetic. It is also shown that there are compact extraresolvable spaces \(X\) with \(|X|=\Delta \), \(X=2^\kappa \), and extraresolvable topological Abelian groups having various properties.
reviewed by: M. Hušek
description: scientific article; zbMATH DE number 1682890