Geodesic
On universality of finite powers of locally path-connected meager spaces
Taras Banakh 1   ; Robert Cauty 2
1 Department of Mathematics Lviv National University Universytetska 1 Lviv 79000, Ukraine and Instytut Matematyki Akademia /Swi/etokrzyska Kielce, Poland
2 Université Paris VI UFR 920, Boîte courrier 172 4, Place, Jussieu 75252 Paris Cedex 05, France
Colloquium Mathematicum, Tome 102 (2005) no. 1, pp. 87-95 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $n$.
DOI : 10.4064/cm102-1-8
Keywords: shown every integer power locally path connected metrizable space first baire category mathcal universal contains closed topological copy each n dimensional metrizable sigma compact space one dimensional sigma compact absolute retract found power mathcal universal every

Taras Banakh  1   ; Robert Cauty  2

1 Department of Mathematics Lviv National University Universytetska 1 Lviv 79000, Ukraine and Instytut Matematyki Akademia /Swi/etokrzyska Kielce, Poland
2 Université Paris VI UFR 920, Boîte courrier 172 4, Place, Jussieu 75252 Paris Cedex 05, France 
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 locally path-connected meager spaces
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Taras Banakh; Robert Cauty. On universality of finite powers of
 locally path-connected meager spaces. Colloquium Mathematicum, Tome 102 (2005) no. 1, pp. 87-95. doi: 10.4064/cm102-1-8

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