Cleavability in semigroups
type: Item
instance of: scholarly article
title: Cleavability in semigroups
zbMATH Open document ID: 0953.22003
DOI: 10.1007/PL00006016
author: N. Delaunay
published in: Semigroup Forum
publication date: 2001-01-22T00:00:00Z
review text: The notion of cleavability was originally introduced in topology: a space \(X\) is cleavable (pointwise cleavable) over a class \(\mathcal P\) of topological spaces if for every \(A \subset X\) (every \(x\in X\)) there exist \(Y\in\mathcal P\) and a continuous mapping \(f:X\to Y\) such that \(f^\gets f(A)=A\) (\(f^\gets f(x)=x\)). By replacing ``topological space'' by ``semigroup'' and ``continuous mapping'' by ``semigroup homomorphism'' the authors define cleavability of semigroups and prove two results of the following sort: If a semigroup \(S\) is (pointwise) cleavable over a class \(\mathcal P\) of semigroups, then \(S\) is so in \(\mathcal P\).
Mathematics Subject Classification ID: 22A15
zbMATH DE Number: 1491102
zbMATH Keywords: cleavability
zbMATH Keywords: pointwise cleavability
zbMATH Keywords: semigroup
zbMATH Keywords: ordered topological semilattice
reviewed by: Ljubiša D. R. Kočinac
MaRDI profile type: Publication
full work available at URL: pl00006016
OpenAlex ID: W2025667608
description: scientific article; zbMATH DE number 1491102