2021/10/05 by Тарас Банах, Banakh, Taras, Alex Ravsky +1
Decision Sciences · Mathematics · #22A15 #54D10 #54H11 #Advanced Topology and Set Theory #FOS: Mathematics #Fuzzy and Soft Set Theory #General Topology (math.GN) #Group Theory (math.GR) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2110.02303
openalex publication_date 2021/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a paratopological group. Following F. Lin and S. Lin, we say that the group G is pseudobounded, if for any neighborhood U of the identity of G, there exists a natural number n such that Un=G. The group G is ω-pseudobounded, if for any neighborhood U of the identity of G, the group G is a union of sets Un, where n is a natural number. The group G is premeager, if G≠ Nn for any nowhere dense subset N of G and any positive integer n. In this paper we investigate relations between the above classes of groups and answer some questions posed by F. Lin, S. Lin, and Sánchez.