A nontrivial pairing of finite \(T_0\) spaces
type: Item
instance of: scholarly article
title: A nontrivial pairing of finite \(T_0\) spaces
zbMATH Open document ID: 1018.55007
DOI: 10.1016/S0166-8641(01)00298-X
author: J. J. C. Vermeulen
author: K. A. Hardie
author: P. J. Witbooi
published in: Topology and its Applications
publication date: 2003-03-10T00:00:00Z
review text: A map of pointed spaces \(\mu:X\times Y\to Z\) is called a pairing with axes \(f:X\to Z\) and \(g:Y\to Z\) if \(\mu\) restricted to \(X\vee Y\) is homotopic to \(f\vee g\). This paper exhibits examples of nontrivial connected finite \(T_0\)-spaces \(X\) and \(Z\) that admit a pairing \(\mu:X\times X\to Z\) with axes \(f\) and \(f\) where \(f:X\to Z\) is a weak homotopy equivalence. The authors propose this concept as a good notion of \(H\)-space for finite spaces. They use it to exhibit finite space realizations of the product on \(S^1\), the Hopf map \(S^3\to S^2\), and the spaces \(\mathbb{R} P^2\) and \(\mathbb{C} P^2\).
Mathematics Subject Classification ID: 55P45
Mathematics Subject Classification ID: 06A07
Mathematics Subject Classification ID: 55Q40
Mathematics Subject Classification ID: 55R65
zbMATH DE Number: 1879144
zbMATH Keywords: \(H\)-space
zbMATH Keywords: barycentric subdivision
zbMATH Keywords: Hopf construction
zbMATH Keywords: Hopf map
zbMATH Keywords: poset
zbMATH Keywords: quasifibration
zbMATH Keywords: simplicial complex
zbMATH Keywords: pairing with axes
zbMATH Keywords: finite spaces
zbMATH Keywords: finite space realizations
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1879144