arXiv subjects

A. Kucharski

Publications and source records attributed to A. Kucharski.

3 recordsLinked to original sources

arXiv2012

Skeletally Dugundji spaces

We introduce and investigate the class of skeletally Dugundji spaces as a skeletal analogue of Dugundji space. The main result states that the following conditions are equivalent for a given space $X$: (i) $X$ is skeletally Dugundji; (ii) Every compactification of $X$ is co-absolute to a Dugundji space; (iii) Every $C^*$-embedding of the absolute $p(X)$ in another space is strongly $π$-regular; (iv) $X$ has a multiplicative lattice in the sense of Shchepin \cite{s76} consisting of skeletal maps.

math.GN↗

arXiv2010

Very I-favorable spaces

We prove that a Hausdorff space $X$ is very $\mathrm I$-favorable if and only if $X$ is the almost limit space of a $σ$-complete inverse system consisting of (not necessarily Hausdorff) second countable spaces and surjective d-open bonding maps. It is also shown that the class of Tychonoff very $\mathrm I$-favorable spaces with respect to the co-zero sets coincides with the d-openly generated spaces.

math.GN↗

arXiv2006

Game Approach to Universally Kuratowski-Ulam Spaces

We consider a version of the open-open game, indicating its connections with universally Kuratowski-Ulam spaces. We show that: Every I-favorable space is universally Kuratowski-Ulam, (Theorem 8); If a compact space Y is I-favorable, then the hyperspace exp(Y) with the Vietoris topology is I-favorable, and hence universally Kuratowski-Ulam, (Theorems 6 and 9). Notions of uK-U and uK-U* spaces are compared.

math.GN↗