A direct proof of a theorem on monotonically normal spaces for GO-spaces
type: Item
instance of: scholarly article
title: A direct proof of a theorem on monotonically normal spaces for GO-spaces
zbMATH Open document ID: 1181.54037
DOI: 10.1216/RMJ-2009-39-6-2067
author: Çetin Vural
published in: Rocky Mountain Journal of Mathematics
publication date: 2010-01-05T00:00:00Z
review text: \textit{Z. Balogh} and \textit{M. E. Rudin} have proved in [Topology Appl. 47, No. 2, 115--127 (1992; Zbl 0769.54022)] that any monotonically normal space \(X\) has the following property: Every open cover of \(X\) has a \(\sigma\)-disjoint open partial refinement \(\mathcal V\) such that \(X\setminus \cup{\mathcal V}\) is the union of a discrete family of closed subspaces which are homeomorphic to some stationary subset of a regular uncountable cardinal. In particular, since any GO-space is monotonically normal, GO-spaces have this property. In the present paper the author gives a direct proof of this fact.
reviewed by: Jorge Picado
Mathematics Subject Classification ID: 54F05
Mathematics Subject Classification ID: 54D20
zbMATH DE Number: 5652738
zbMATH Keywords: GO-space
zbMATH Keywords: refinement
zbMATH Keywords: stationary set
MaRDI profile type: Publication
cites work: Monotone normality
cites work: Q3906758
cites work: Monotonically Normal Spaces
cites work: Q3925533
full work available at URL: rmj-2009-39-6-2067
OpenAlex ID: W2000999262
Recommended article: The \(\beta\)-space property in monotonically normal spaces and go-spaces
Recommended article: A note on monotonically normal spaces
Recommended article: Q3790302
Recommended article: Q5112608
Recommended article: Compactifications and remainders of monotonically normal spaces
Recommended article: Monotone normality in generalized topological spaces
Recommended article: Q3825732
Recommended article: On (monotonically) metacompact subspaces of GO-spaces and related conclusions
Recommended article: Q4228859
Recommended article: Q3593926
description: scientific article; zbMATH DE number 5652738