Speciality:
01.01.06 (Mathematical logic, algebra, and number theory)
E-mail: ,
Keywords: universal algebra; lattices connected with algebraic systems; unary algebras; topological algebraic systems.
Subject:
In a number of papers we investigate lattices of topologies on algebras and especially lattices of topologies on unars (i.e., on algebras with one unary operation). Some finiteness conditions on these lattices are studied. The sets of all atoms of lattices of topologies on unars are described. Characterizations of those unars whose lattices of topologies are modular, distributive, complemented, pseudocomplemented, Boolean or chains are obtained. We give necessary and sufficient conditions for a modular lattice to be isomorphic to a lattice of topologies of some unar. The sets of all T_0$, $T_1$, and $T_2$-topologies are also considered.
Main publications:
Kartashova A. V. Cardinalities of lattices of topologies of unars and some related topics // Discussiones Mathematicae. General Algebra and Applications, 2001, 21.
