2022/04/05 by Meng Bao, Bao, Meng, Xuewei Ling +3 · 1 citation
Computer Science · Decision Sciences · Mathematics · #18A32 #20B30 #20N05 #22A22 #54A20 #Advanced Algebra and Logic #FOS: Mathematics #Fuzzy and Soft Set Theory #General Topology (math.GN) #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2204.02079
openalex publication_date 2022/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we mainly investigate the quotient spaces G/H when G is a strongly topological gyrogroup and H is a strong subgyrogroup of G. It is shown that if G is a strongly topological gyrogroup, H is a closed strong subgyrogroup of G and H is inner neutral, then the quotient space G/H is first-countable if and only if G/H is a bisequential space if and only if G/H is a weakly first-countable space if and only if G/H is a csf-countable and sequential a7-space. Moreover, it is shown that if H is a locally compact metrizable strong subgyrogroup of G and the quotient space G/H is sequential, then G is also sequential; if H is a closed first-countable and separable strong subgyrogroup of G, the quotient space G/H is a cosmic space, then G is also a cosmic space; if the quotient space G/H has a star-countable cs-network or star-countable wcs*-network, then G also has a star-countable cs-network or star-countable wcs*-network, respectively.