On atoms in topology lattices of unary algebras
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.
scientific article; zbMATH DE number 5319744
scientific article