Some characterizations of regular ω-balanced paratopological groups with a q-point

• Ni, Hanyi ^[1] ; Xie, Li-Hong ^[1] ; Jin, Yingying ^[2]
  1. [1] Wuyi University
  2. [2] Guangzhou Polytechnic University
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 27, Nº. 2, 2026
• Idioma: inglés
• DOI: 10.4995/agt.26582
• Enlaces
  • Texto completo
• Resumen

  • In this paper, the regular ω -balanced paratopological groups with a q-point are investigated. We mainly show that: (1) a paratopological group G is a regular ω-balanced q-space with S m ( G ) ≤ ω iff for each open neighborhood O of the identity e in G there is a closed countably compact invariant subgroup H ⊆ O of G such that the quotient space G/H is a regular and quasi-metrizable paratopological group while the canonical quotient mapping p : G → G / H is open and quasi-perfect; (2) a paratopological group G is a regular ω-balanced strong q-space iff each open neighborhood O of e contains a closed sequentially compact neutral subgroup H of countable character, which is a strong q-sequence at each y ∈ H such that H ⊆ O, the quotient space G/H is a regular and quasi-metrizable paratopological group while the canonical quotient mapping p : G → G / H is open and strongly sequential-perfect; (3) a regular paratopological group G is an ω-balanced pointwise pseudocompact space with S m ( G ) ≤ ω iff for every open neighborhood O of the identity e in G, there exists a closed r-pseudocompact invariant subgroup H ⊆ O and a sequence { Wn : n ∈ ω } of open neighborhoods of H, such that every family { On : n ∈ ω } of non-empty open sets with On ⊆ Wn for each n ∈ ω has an accumulation point in H that Wn = Wn H for each n ∈ ω and the quotient space G/H is an ω-balanced pointwise pseudocompact space in which every point is a regular Gδ -set.These results extend the characterizations of q-spaces, strict q-spaces, and strong q-spaces established by [3] to the class of ω-balanced paratopological groups.

     

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