VSE knjižnice (vzajemna bibliografsko-kataložna baza podatkov COBIB.SI)
PDF
  • Weak completions of paratopological groups
    Banakh, Taras, 1968- ; Tkachenko, Mikhail
    Given a ▫$T_0$▫ paratopological group $G$ and a class ▫$\mathscr{C}$▫ of continuous homomorphisms of paratopological groups, we define the ▫$\mathscr{C}$▫-semicompletion ▫$\mathscr{C}[G)$▫ and ... ▫$\mathscr{C}$▫-completion ▫$\mathscr{C}[G]$▫ of the group ▫$G$▫ that contain ▫$G$▫ as a dense subgroup, satisfy the ▫$T_0$▫-separation axiom and have certain universality properties. For special classes ▫$\mathscr{C}$▫, we present some necessary and sufficient conditions on ▫$G$▫ in order that the (semi)completions ▫$\mathscr{C}[G)$▫ and ▫$\mathscr{C}[G]$▫ be Hausdorff. Also, we give an example of a Hausdorff paratopological abelian group ▫$G$▫ whose ▫$\mathscr{C}$▫-semicompletion ▫$\mathscr{C}[G)$▫ fails to be a ▫$T_1$▫-space, where ▫$\mathscr{C}$▫ is the class of continuous homomorphisms of sequentially compact topological groups to paratopological groups. In particular, the group ▫$G$▫ contains an ▫$\omega$▫-bounded sequentially compact subgroup ▫$H$▫ such that ▫$H$▫ is a topological group but its closure in ▫$G$▫ fails to be a subgroup.
    Vir: Topology and its Applications. - ISSN 0166-8641 (Vol. 304, Dec. 2021, art. 107797 (9 str.))
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2021
    Jezik - angleški
    COBISS.SI-ID - 71355651

    Povezava(-e):

    https://www.sciencedirect.com/science/article/pii/S0166864121002121
    DOI

vir: Topology and its Applications. - ISSN 0166-8641 (Vol. 304, Dec. 2021, art. 107797 (9 str.))
loading ...
loading ...
loading ...

Vnos na polico