Bijectively related spaces. I: Manifolds
type: Item
instance of: scholarly article
title: Bijectively related spaces. I: Manifolds
zbMATH Open document ID: 0554.57014
author: Patrick H. Doyle
author: J. G. Hocking
published in: Pacific Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: Two Hausdorff spaces X and Y are bijectively related if there exist continuous bijections \(f: X\to Y\) and \(g: Y\to X\). The authors show that there exist non-homeomorphic connected bijectively related n-manifolds for each \(n\geq 2\). Starting from this fact, they mention many properties with respect to reversibility for connected manifolds. The following is one of typical results: If the manifold M has only compact boundary components and if M is simply connected, then M is reversible, that is, the only continuous self-bijections \(f: M\to M\) are the homeomorphisms.
Mathematics Subject Classification ID: 57N15
Mathematics Subject Classification ID: 54C10
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57N05
zbMATH DE Number: 3883218
zbMATH Keywords: non-homeomorphic connected bijectively related n-manifolds
zbMATH Keywords: reversibility for connected manifolds
MaRDI profile type: Publication
full work available at URL: pjm.1984.111.23
OpenAlex ID: W1984811408
DOI: 10.2140/PJM.1984.111.23
description: scientific article; zbMATH DE number 3883218