Infinite-dimensional manifolds related to C-spaces

Abstract

Haver's property C turns out to be related to Borst's transfinite extension of the covering dimension. We prove that, for a uncountably many countable ordinals β there exists a strongly universal kω-space for the class of spaces of transfinite covering dimension <β. In some sense, our result is a kω-counterpart of Radul's theorem on existence of absorbing sets of given transfinite covering dimension.