Feathered gyrogroups and gyrogroups with countable pseudocharacter

2019/11/29 by Meng Bao, Bao, Meng, Fucai Lin +1 · 4 citations
Computer Science · Mathematics · #26A03 #40A05 #40A30 #40A99 #FOS: Mathematics #General Topology (math.GN) #Group Theory (math.GR) #Logic, programming, and type systems #Mathematics and Applications #Primary 54A20 #secondary 11B05 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1911.12938

openalex publication_date 2019/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Topological gyrogroups, with a weaker algebraic structure than groups, have been investigated recently. In this paper, we prove that every feathered strongly topological gyrogroup is paracompact, which implies that every feathered strongly topological gyrogroup is a D-space and gives partial answers to two questions posed by A.V.Arhangel' ski\vı~(2010) in \citeAA1. Moreover, we prove that every locally compact NSS-gyrogroup is first-countable. Finally, we prove that each Lindelöf P-gyrogroup is Ra\check\imathkov complete.

Cited by

• Weak countability axioms on the quotient spaces of topological gyrogroups
• Strongly topologically orderable gyrogroups with a suitable set
• The existence of suitable sets in locally compact strongly topological gyrogroups
• Subgyrogroups within the product spaces of paratopological gyrogroups

Related

• A supplement on feathered gyrogroups
• On paratopological gyrogroups
• Submetrizability of strongly topological gyrogroups
• Quotient with respect to admissible L-subgyrogroups
• On the continuity of the inverse in (strongly) paratopological gyrogroups