A note on feebly compact semitopological symmetric inverse semigroups of a bounded finite rank

DOI10.30970/VMM.2021.91.040-053zbMATH Open1499.22004arXiv2202.08308MaRDI QIDQ5084815

Oleg Gutik

Publication date: 28 June 2022

Published in: Visnyk Lvivskogo Universytetu Seriya Mekhaniko-Matematychna (Search for Journal in Brave)

Abstract: We study feebly compact shift-continuous $T_1$-topologies on the symmetric inverse semigroup $mathscr{I}_{l}ambd{a}^n$ of finite transformations of the rank $leqslantn$. It is proved that such $T_1$-topology is sequentially pracompact if and only if it is feebly compact. Also, we show that every shift-continuous feebly $omega$-bounded $T_1$-topology on $mathscr{I}_{l}ambd{a}^n$ is compact.

Full work available at URL: https://arxiv.org/abs/2202.08308

zbMATH Keywords

semigroupproductsemitopological semigroupcompactinverse semigroupfeebly compact\(\omega\)-bounded pracompact\(\sum\)-productfeebly \(\omega\)-boundedsequentially pracompactthe Sunflower Lemmatotally countably pracompact

Mathematics Subject Classification ID

Compactness (54D30) Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) (54A10) Remainders in general topology (54D40) Structure of topological semigroups (22A15) Local compactness, (sigma)-compactness (54D45) Topological representations of algebraic systems (54H10)

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