2024/06/11 by Fucai Lin, Lin, Fucai, Xixi Qi +1
Decision Sciences · Mathematics · #22A05 #54B15 #54E35 #Advanced Topology and Set Theory #FOS: Mathematics #Fixed Point Theorems Analysis #Fuzzy and Soft Set Theory #General Topology (math.GN) #Group Theory (math.GR) #Primary 54H11 #secondary 54A25
paper · pdf · doi:10.48550/arxiv.2406.06927
openalex publication_date 2024/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A semitopological group G is called \it an n-semitopological group, if for any g∈ G with e\not∈\g\ there is a neighborhood W of e such that g\not∈ Wn, where n∈ℕ. The class of n-semitopological groups (n≥ 2) contains the class of paratopological groups and Hausdorff quasi-topological groups. Fix any n∈ℕ. Some properties of n-semitopological groups are studied, and some questions about n-semitopological groups are posed. Some generalized metric properties of n-semitopological groups are discussed, which contains mainly results are that (1) each Hausdorff first-countable 2-semitopological group admits a coarsersemi-metrizable topology; (2) each locally compact, Baire and σ-compact 2-semitopological group is a topological group; (3) the condensation of some kind of 2-semitopological groups topologies are given. Finally, some cardinal invariants of n-semitopological groups are discussed.