A group of continuous self-maps on a topological groupoid
type: Item
instance of: scholarly article
title: A group of continuous self-maps on a topological groupoid
zbMATH Open document ID: 1393.22002
author: Habib Amiri
published in: Semigroup Forum
publication date: 2018-06-13T00:00:00Z
review text: Let \(G\) be a topological groupoid, and let \(G^{2}\) denote the groupoid of all composable pairs in \(G\times G\). It is proved in this work that the group of bisections of \(G^{2}\) is isomorphic to the group of units in the monoid \(S_{G} = \{ f:G \to G \;: \;f \text{ is continuous, and } (x,f(x)) \in G^{2} \text{ for every } x \in G \}\). In addition, it is proved further that the group of transitive bisections of \(G\) can be embedded in \(S_{G}\).
reviewed by: Watchareepan Atiponrat
Mathematics Subject Classification ID: 22A22
zbMATH DE Number: 6888056
zbMATH Keywords: topological semigroup
zbMATH Keywords: Topological groupoid
zbMATH Keywords: group of bisections
MaRDI profile type: Publication
full work available at URL: s00233-017-9857-6
OpenAlex ID: W2592851136
cites work: Q3994935
cites work: Haar Measure for Measure Groupoids
cites work: Q4856603
cites work: The Lie group of bisections of a Lie groupoid
DOI: 10.1007/S00233-017-9857-6
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description: scientific article; zbMATH DE number 6888056