26 citations · 49 across the 8 of their papers we have counts for
10 papers
Remarks on asymptotic power dimension
Jacek Kucab, Michael Zarichnyi
Using a result of Dranishnikov and Smith we prove that, under some conditions, the asymptotic power dimension of a proper metric space coincides with the dimension of its subpower…
Asymptotic dimension, decomposition complexity, and Haver's property C
Alexander Dranishnikov, Michael Zarichnyi
The notion of the decomposition complexity was introduced in \cite{GTY} using a game theoretical approach. We introduce a notion of straight decomposition complexity and compare it…
On asymptotic extension dimension
Dušan Repovš, Mykhailo Zarichnyi
The aim of this paper is to introduce an asymptotic counterpart of the extension dimension defined by Dranishnikov. The main result establishes a relation between the asymptotic ex…
On monomorphic topological functors with finite supports
Taras Banakh, Marta Martynenko, Michael Zarichnyi
We prove that a monomorphic functor with finite supports is epimorphic, continuous, and its maximal -modification preserves intersections. Thi…
Spaces of idempotent measures of compact metric spaces
Lidia Bazylevych, Dušan Repovš, Michael Zarichnyi
We investigate certain geometric properties of the spaces of idempotent measures. In particular, we prove that the space of idempotent measures on an infinite compact metric space…
Hyperspace of convex compacta of nonmetrizable compact convex subspaces of locally convex spaces
Lidia Bazylevych, Dušan Repovš, Michael Zarichnyi
Our main result states that the hyperspace of convex compact subsets of a compact convex subset in a locally convex space is an absolute retract if and only if is an absolu…