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 𝓐₁[n]-universal, i.e., contains a closed topological copy of each at most n-dimensional metrizable σ-compact space. Also a one-dimensional σ-compact absolute retract X is found such that the power X^{n+1} is 𝓐₁[n]-universal for every n.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm102-1-8,
author = {Taras Banakh and Robert Cauty},
title = {On universality of finite powers of locally path-connected meager spaces},
journal = {Colloquium Mathematicae},
volume = {103},
year = {2005},
pages = {87-95},
zbl = {1078.54022},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm102-1-8}
}
Taras Banakh; Robert Cauty. On universality of finite powers of locally path-connected meager spaces. Colloquium Mathematicae, Tome 103 (2005) pp. 87-95. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm102-1-8/