arXiv subjects

Konstantin Kazachenko

Publications and source records attributed to Konstantin Kazachenko.

3 recordsLinked to original sources

arXiv2026

Idempotent Ultrafilters and Closed Images of Complete Semilattices

We prove that every continuous homomorphism from a complete topologized semilattice to a Hausdorff semitopological semilattice has closed image, answering a question of Banakh and Bardyla. The main step is the convergence of idempotent ultrafilters on complete semitopological semilattices. We also prove that, for every complete subsemilattice $X$ of a Hausdorff semitopological semilattice $Y$, the natural order of $X$ is closed in $Y\times Y$. In particular, the natural order of every complete Hausdorff semitopological semilattice $X$ is closed in $X\times X$.

math.RA↗

arXiv2023

Joint continuity in semitopological monoids and semilattices

In this paper we study the separately continuous actions of semitopological monoids on pseudocompact spaces. The main aim of this paper is to generalize Lawson's results to some class of pseudocompact spaces. Also, we introduce a concept of a weak $q_D$-space and prove that a pseudocompact space and a weak $q_D$-space form a Grothendieck pair. As an application of the main result, we investigate the continuity of multiplication and taking inverses in subgroups of semitopological semigroups. In particular, we get that if $(S,\bullet)$ is a Tychonoff pseudocompact semitopological monoid with a quasicontinuous multiplication $\bullet$ and $G$ is a subgroup of $S$, then $G$ is a topological group. Also, we study the continuity of operations in semitopological semilattices.

math.GN↗

arXiv2021

Various types of completeness in topologized semilattices

A topologized semilattice $X$ is called complete if each non-empty chain $C\subset X$ has $\inf C$ and $\sup C$ that belong to the closure $C$ of the chain $C$ in $X$. In this paper, we introduce various concepts of completeness of topologized semilattices in the context of operators that generalize the closure operator, and study their basic properties. In addition, examples of specific topologized semilattices are given, showing that these classes do not coincide with each other. Also in this paper, we prove theorems that allow us to generalize the available results on complete semilattices endowed with topology.

math.RA↗