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17 papers · 1 filter
Convex hyperspaces of probability measures and extensors in the asymptotic category
Dušan Repovš, Mykhailo Zarichnyi
The objects of the Dranishnikov asymptotic category are proper metric spaces and the morphisms are asymptotically Lipschitz maps. In this paper we provide an example of an asymptot…
Fuzzy Prokhorov metric on the set of probability measures
D. Repovš, A. Savchenko, M. Zarichnyi
We introduce a fuzzy metric on the set of probability measures on a fuzzy metric space. The construction is an analogue, in the realm of fuzzy metric spaces, of the Prokhorov metri…
On the singular homology of one class of simply-connected cell-like spaces
Katsuya Eda, Umed H. Karimov, Dušan Repovš
In our earlier papers we constructed examples of 2-dimensional nonaspherical simply-connected cell-like Peano continua, called {\sl Snake space}. In the sequel we introduced the fu…
On M-separability of countable spaces and function spaces
Dušan Repovš, Lyubomyr Zdomskyy
We study M-separability as well as some other combinatorial versions of separability. In particular, we show that the set-theoretic hypothesis b=d implies that the class of selecti…
A new Lindelof topological group
Dusan Repovs, Lyubomyr Zdomskyy
We show that the subsemigroup of the product of w_1-many circles generated by the L-space constructed by J. Moore is again an L-space. This leads to a new example of a Lindelof top…
Uniform convexity and the splitting problem for selections
Maxim V. Balashov, Dušan Repovš
We continue to investigate cases when the Repovš-Semenov splitting problem for selections has an affirmative solution for continuous set-valued mappings. We consider the situation…