(UL)
  • On cardinal invariants and metrizability of topological inverse Clifford semigroups
    Banakh, Taras, 1968-
    Let ▫$S$▫ be a compact topological inverse Clifford semigroup such that the maximal semilattice ▫$E$▫ and all maximal groups of ▫$S$▫ are metrizable. We prove that ▫$S$▫ is first countable and has ... countable cellularity; moreover, ▫$S$▫ is metrizable, provided one of the following conditions is satisfied: (1) (MA+▫$\neg$▫CH) holds; (2) ▫$E$▫ is a ▫$G_\delta$▫-set in ▫$S$▫; (3) ▫$E$▫ is zero-dimensional; (4) ▫$E$▫ is a Lawson semilattice; (4) all maximal groups of ▫$S$▫ are Lie groups; (5) ▫$S$▫ is dyadic or scadic compact; (6) ▫$S$▫ is a fragmentable (or Rosenthal) monolithic compactum; (7) ▫$S$▫ is a Corson (or Rosenthal) compactum with countable spread. Under CH two (separable and unseparable) compact non-metrizable topological inverse commutative semigroups with metrizable subsemilattices and subgroups are constructed. One of these semigroups is a first-countable ccc Corson compact space satisfying the properties (M), ▫$(*)$▫ and $(K_n)$ for all ▫$n\ge 2$▫ but failing ▫$(**)$▫.
    Vir: Topology and its Applications. - ISSN 0166-8641 (Vol. 128, iss. 1, 2003, str. 13-48)
    Vrsta gradiva - članek, sestavni del
    Leto - 2003
    Jezik - angleški
    COBISS.SI-ID - 15765593

    Povezava(-e):

    http://dx.doi.org/10.1016/S0166-8641(02)00083-4

vir: Topology and its Applications. - ISSN 0166-8641 (Vol. 128, iss. 1, 2003, str. 13-48)

loading ...
loading ...
loading ...

Vnos na polico