@article{Lin2025, 
author = {Kaixiong Lin and Jing Zhang and Hanfeng Wang},
title = {Some results in generalized topological groups},
year = {2025},
journal = {Electronic Research Archive},
volume = {33},
number = {10},
pages = {6206-6218},
keywords = {generalized topology groups, coset spaces, total disconnectedness, cardinal invariants, metrizability},
url = {https://www.sciopen.com/article/10.3934/era.2025274},
doi = {10.3934/era.2025274},
abstract = {It is proved in this paper that if    G is a        G  -topological group and    {      K          i        :  i  ∈  ω  } is a family of generalized open subsets containing the identity element    e in    G satisfying        K          i      +      1        2    ⊂      K    i   and        K    i          −      1        =      K    i   for every    i  ∈  ω, then    G      /    H is metrizable where    H  =      ⋂          i      ∈      ω            K          i      . Let        (          G      ,      τ        )   be a        G  -topological group satisfying for every    e  ∈  U  ∈  τ that there is    e  ∈  O  ∈  τ such that        O          2        ⊂  U. Then, we obtain that 1) if    H is generalized    κ-narrow and    c      l          G        H  =  G, then    G is also generalized    κ-narrow; 2)    A  B is generalized    κ-narrow in    G provided that    A and    B are generalized    κ-narrow in    G. Finally, we consider coset spaces. It is shown that 3) for a subgroup    H of G, if H and the generalized quotient space G/H have countable generalized pseudocharacter, then G also has countable generalized pseudocharacter; 4) for a subgroup    H, if    H is the generalized connected component containing    e in    G,    G      /    H is generalized totally disconnected; 5) if H is a generalized closed subgroup and generalized totally disconnected, then G is also generalized totally disconnected when G/H is generalized totally disconnected.}
}