Diagonal structures on topological spaces
type: Item
instance of: scholarly article
title: Diagonal structures on topological spaces
zbMATH Open document ID: 1024.54018
DOI: 10.1016/S0166-8641(01)00289-9
published in: Topology and its Applications
publication date: 2003-03-10T00:00:00Z
review text: The author develops some ideas and techniques from his paper [Appl. Gen. Topol. 1, 13-28 (2000; Zbl 0991.54027)]. He investigates when a topological space admits a partial product operation satisfying some rather weak continuity restrictions and almost nothing else, the only algebraic requirement being that some element \(e\) of \(X\) is a left and right identity with respect to this multiplication. The operation is called partial diagonalization of \(X\) at \(e\). Several sufficient conditions for a space to be partially diagonalizable are established. On the other hand, it is shown that certain deep results about the topological structure of compact topological groups can be extended to partially diagonalizable compact spaces. It is also shown that partial diagonalizability playes an important role in some classical topics of general topology. In the final section some open questions are discussed.
Mathematics Subject Classification ID: 54D50
Mathematics Subject Classification ID: 54D60
Mathematics Subject Classification ID: 54H11
Mathematics Subject Classification ID: 54C35
zbMATH DE Number: 1879135
zbMATH Keywords: partial diagonalizability
zbMATH Keywords: folding
zbMATH Keywords: homogeneous space
zbMATH Keywords: Stone-Čech compactification
zbMATH Keywords: Moscow space
zbMATH Keywords: weakly Klebanov space
zbMATH Keywords: power homogeneity
zbMATH Keywords: Hewitt-Nachbin completion
zbMATH Keywords: \(\delta\)-tightness
zbMATH Keywords: \(C\)-embedding
zbMATH Keywords: separability
zbMATH Keywords: pseudocompact space
author: A. V. Arhangel'skii
reviewed by: Shou Lin
MaRDI profile type: Publication
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full work available at URL: s0166-8641(01)00289-9
OpenAlex ID: W2027238895
description: scientific article; zbMATH DE number 1879135