On atoms in topology lattices of unary algebras
type: Item
instance of: scholarly article
title: On atoms in topology lattices of unary algebras
zbMATH Open document ID: 1169.08003
author: A. V. Kartashova
published in: Journal of Mathematical Sciences (New York)
publication date: 2008-09-03T00:00:00Z
review text: Assume that \((A,\Sigma)\) is an algebra. A topology on the set \(A\), such that each operation from \(\Sigma\) is continuous with respect to this topology, is called a topology on the algebra \((A,\Sigma)\). The topologies on the algebra \((A,\Sigma)\) form a complete lattice with respect to inclusion. This lattice is called the topology lattice of the given algebra. In this paper, the topology lattice of algebras with one unary operation (unars) is studied. A necessary and sufficient condition is found that the set of atoms of the topology lattice of a unar is finite or countable.
Mathematics Subject Classification ID: 08A60
Mathematics Subject Classification ID: 22A30
Mathematics Subject Classification ID: 54A10
zbMATH DE Number: 5319744
zbMATH Keywords: unary algebra
zbMATH Keywords: topology lattice
zbMATH Keywords: atom
zbMATH Keywords: topology generated by congruence
reviewed by: Yuri Movsisyan
MaRDI profile type: Publication
full work available at URL: s10958-007-0220-4
OpenAlex ID: W2022625222
cites work: Subalgebra lattices of mono-unary algebras
cites work: Q3495406
cites work: On the Congruence Lattices of Unary Algebras
cites work: Q3866167
cites work: On lattices of topologies of unary algebras
cites work: \(| End A | = | Con A | = | Sub A | = 2^{| A|}\) for any uncountable 1-unary algebra
cites work: Congruences and quasiidentities on unars
DOI: 10.1007/S10958-007-0220-4
Recommended article: On lattices of topologies of unary algebras
Recommended article: Topology lattices of unary algebras
Recommended article: On congruence lattices and topology lattices of unary algebras
Recommended article: On finite lattices of topologies of commutative unary algebras
Recommended article: Lattices of topologies of unary algebras of the variety \(\mathcal A_{1,1}\)
Recommended article: On atoms in the lattice of quasivarieties
Recommended article: Q3718775
Recommended article: Q4660058
Recommended article: Q3095886
Recommended article: On the lattices of \(L\)-topologies
description: scientific article; zbMATH DE number 5319744