On universality of finite powers of locally path-connected meager spaces

Tom 102 / 2005

Taras Banakh, Robert Cauty Colloquium Mathematicum 102 (2005), 87-95 MSC: 54F45, 54B10, 54F50, 54H05, 54C55, 54D45, 57N20. DOI: 10.4064/cm102-1-8

Streszczenie

It is shown that for every integer $n$ the $(2n+1)$th power of any locally path-connected metrizable space of the first Baire category is ${\mathcal A}_1[n]$-universal, i.e., contains a closed topological copy of each at most $n$-dimensional metrizable $\sigma $-compact space. Also a one-dimensional $\sigma $-compact absolute retract $X$ is found such that the power $X^{n+1}$ is ${\mathcal A}_1[n]$-universal for every $n$.

Autorzy

  • Taras BanakhDepartment of Mathematics
    Lviv National University
    Universytetska 1
    Lviv 79000, Ukraine
    and
    Instytut Matematyki
    Akademia /Swi/etokrzyska
    Kielce, Poland
    e-mail
  • Robert CautyUniversité Paris VI
    UFR 920, Boîte courrier 172
    4, Place, Jussieu
    75252 Paris Cedex 05, France
    e-mail

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