Coset spaces of metrizable groups

Sergey Antonyan, Natella Antonyan, Konstantin L. Kozlov Colloquium Mathematicum MSC: Primary 54H15, 22F30; Secondary 54D35, 57S05. DOI: 10.4064/cm7963-8-2020 Published online: 15 March 2021

Abstract

We characterize topological spaces which are coset spaces of (separable) metrizable groups and complete metrizable (Polish) groups. Moreover, it is shown that for a $G$-space $X$ with a $d$-open action there is a topological group $H$ of weight and cardinality less than or equal to the weight of $X$ such that $H$ admits a $d$-open action on $X$. This is further applied to show that if $X$ is a separable metrizable coset space of some topological group, then $X$ has a Polish extension which is a coset space of a Polish group.

Authors

  • Sergey AntonyanDepartment of Mathematics
    Xi’an Technological University
    Xi’an, Shaanxi, 710021, P.R. China
    and
    Moscow Center for Fundamental
    and Applied Mathematics
    Moscow, Russia
    and
    Departamento de Matemáticas
    Facultad de Ciencias
    Universidad Nacional Autónoma de México
    04510 Ciudad de México, Mexico
    e-mail
  • Natella AntonyanEscuela de Ingeniería y Ciencias
    Tecnológico de Monterrey
    Campus Ciudad de México
    14380 Ciudad de México, Mexico
    e-mail
  • Konstantin L. KozlovFaculty of Mechanics and Mathematics
    Moscow State University
    Moscow, Russia
    and
    Moscow Center for Fundamental and Applied Mathematics
    Moscow, Russia
    e-mail

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