On universality of finite powers of locally path-connected meager spaces
Volume 102 / 2005
Colloquium Mathematicum 102 (2005), 87-95
MSC: 54F45, 54B10, 54F50, 54H05, 54C55, 54D45, 57N20.
DOI: 10.4064/cm102-1-8
Abstract
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 $n$.
