192 citations · 3.7k across the 290 of their papers we have counts for
15 papers · 2 filters
On continuous choice of retractions onto nonconvex subsets
Dušan Repovš, Pavel V. Semenov
For a Banach space and for a class $\A$ of its bounded closed retracts, endowed with the Hausdorff metric, we prove that retractions on elements $A \in \A$ can be chosen to dep…
On the splitting problem for selections
Maxim V. Balashov, Dušan Repovš
We investigate when does the Repovš-Semenov Splitting problem for selections have an affirmative solution for continuous set-valued mappings in finite-dimensional Banach spaces. We…
The continuity of the inversion and the structure of maximal subgroups in countably compact topological semigroups
Oleg V. Gutik, Dušan Pagon, Dušan Repovš
In this paper we search for conditions on a countably compact (pseudo-compact) topological semigroup under which: (i) each maximal subgroup in is a (closed) topological…
Hartman-Mycielski functor of non-metrizable compacta
Taras Radul, Dušan Repovš
We investigate some topological properties of a normal functor introduced earlier by Radul which is a certain functorial compactification of the Hartman-Mycielski construction…
A unified construction yielding precisely Hilbert and James sequences spaces
Dušan Repovš, Pavel V. Semenov
Following James' approach, we shall define the Banach space for each vector with . The construction immediately implies that…
Packing index of subsets in Polish groups
Taras Banakh, Nadya Lyaskovska, Dušan Repovš
For a subset of a Polish group , we study the (almost) packing index $\ind_P(A)$ (resp. $\Ind_P(A)$) of , equal to the supremum of cardinalities of subsets $S\subse…
On chains in -closed topological pospaces
Oleg V. Gutik, Dušan Pagon, Dušan Repovš
We study chains in an -closed topological partially ordered space. We give sufficient conditions for a maximal chain in an -closed topological partially ordered space suc…
Ernest Michael and theory of continuous selections
Dušan Repovš, Pavel V. Semenov
This is the introductory paper to the special issue of Topology and Its Applications entirely dedicated to the theory of continuous selections of multivalued mappings. Since the pi…
Hereditary invertible linear surjections and splitting problems for selections
Dušan Repovš, Pavel V. Semenov
Let be the pointwise (Minkowski) sum of two convex subsets and of a Banach space. Is it true that every continuous mapping splits into a sum of…
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…
Preserving -sets by Dranishnikov's resolution
S. M. Ageev, M. Cencelj, D. Repovš
We prove that Dranishnikov's -dimensional resolution is a UV-divider of Chigogidze's -dimensional resolution . This fact implies that $d_k^{…
Fréchet-Urysohn fans in free topological groups
Taras Banakh, Dušan Repovš, Lyubomyr Zdomskyy
In this paper we answer the question of T. Banakh and M. Zarichnyi constructing a copy of the Fréchet-Urysohn fan $S_\w$ in a topological group admitting a functorial embedding…
A nonaspherical cell-like 2-dimensional simply connected continuum and related constructions
Katsuya Eda, Umed H. Karimov, Dušan Repovš
We prove the existence of a 2-dimensional nonaspherical simply connected cell-like Peano continuum (the space itself was constructed in one of our earlier papers). We also indicate…
On extending actions of groups
Sergei M. Ageev, Dušan Repovš
Problems of dense and closed extension of actions of compact transformation groups are solved. The method developed in the paper is applied to problems of extension of equivariant…