192 citations · 3.7k across the 290 of their papers we have counts for
47 papers · 1 filter
Preservation of -spaces and covering properties of products
Dušan Repovš, Lyubomyr Zdomskyy
We prove that the Hurewicz property is not preserved by finite products in the Miller model. This is a consequence of the fact that Miller forcing preserves ground model -spaces…
Products of -separable spaces in the Laver model
Dušan Repovš, Lyubomyr Zdomskyy
We prove that in the Laver model for the consistency of the Borel's conjecture, the product of any two -separable spaces is -separable.
Products of Hurewicz spaces in the Laver model
Dušan Repovš, Lyubomyr Zdomskyy
This article is devoted to the interplay between forcing with fusion and combinatorial covering properties. We illustrate this interplay by proving that in the Laver model for the…
Non-meager free sets and independent families
Andrea Medini, Dušan Repovš, Lyubomyr Zdomskyy
Our main result is that, given a collection of meager relations on a Polish space such that , there exists a dense Baire subspace of (…
Sequential rectifiable spaces of countable -character
Taras Banakh, Dusan Repovs
We prove that each non-metrizable sequential rectifiable space of countable -character contains a clopen rectifiable submetrizable -subspace and admits an open d…
Classifying homogeneous cellular ordinal balleans up to coarse equivalence
Taras Banakh, Igor Protasov, Dusan Repovs +1
For every ballean we introduce two cardinal characteristics and describing the capacity of balls in . We observe that these cardinal character…
Classifying homogeneous ultrametric spaces up to coarse equivalence
Taras Banakh, Dušan Repovš
For every metric space we introduce two cardinal characteristics and describing the capacity of balls in . We prove that the…
Productively Lindelöf spaces and the covering property of Hurewicz
Dušan Repovš, Lyubomyr Zdomskyy
We prove that under certain set-theoretic assumptions every productively Lindelöf space has the Hurewicz covering property, thus improving upon some earlier results of Aurichi and…
Countable dense homogeneous filters and the Menger covering property
Dušan Repovš, Lyubomyr Zdomskyy, Shuguo Zhang
In this note we present a ZFC construction of a non-meager filter which fails to be countable dense homogeneous. This answers a question of Hernández-Gutiérrez and Hrušák. The meth…
Continuous selections of multivalued mappings
Dušan Repovš, Pavel V. Semenov
This survey covers in our opinion the most important results in the theory of continuous selections of multivalued mappings (approximately) from 2002 through 2012. It extends and c…
Max-min measures on ultrametric spaces
Matija Cencelj, Dušan Repovš, Mykhailo Zarichnyi
The ultrametrization of the set of all probability measures of compact support on the ultrametric spaces was first defined by Hartog and de Vink. In this paper we consider a simila…
Nonexistence of linear operators extending Lipschitz (pseudo)metric
Dušan Repovš, Mykhailo Zarichnyi
We present an example of a zero-dimensional compact metric space and its closed subspace such that there is no continuous linear extension operator for the Lipschitz pseudo…
Hyperspaces of max-plus convex subsets of powers of the real line
Lidia Bazylevych, Dušan Repovš, Mykhailo Zarichnyi
The notion of max-plus convex subset of Euclidean space can be naturally extended to other linear spaces. The aim of this paper is to describe the topology of hyperspaces of max-pl…
A two-parameter control for contractive-like multivalued mappings
Dušan Repovš
We propose a general approach to defining a contractive-like multivalued mappings which avoids any use of the Hausdorff distance between the sets and . Various fix…
On Pliś metric on the space of strictly convex compacta
Maxim V. Balashov, Dušan Repovš
We consider a certain metric on the space of all convex compacta in , introduced by A. Pliś. The set of strictly convex compacta is a complete metric subspace of the metric…
Topics in uniform continuity
Dikran Dikranjan, Dušan Repovš
This paper collects results and open problems concerning several classes of functions that generalize uniform continuity in various ways, including those metric spaces (generalizin…
Topological monoids of monotone injective partial selfmaps of with cofinite domain and image
Oleg Gutik, Dušan Repovš
In this paper we study the semigroup of partial cofinal monotone bijective transformations of the set of positive integers $\mathbb{N}…
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 the Menger covering property and -spaces
Dušan Repovš, Lyubomyr Zdomskyy
The main results of this note are: It is consistent that every subparacompact space of size is a -space; If there exists a Michael space, then all productively Lindelö…
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…
Direct limit topologies in the categories of topological groups and of uniform spaces
Taras Banakh, Dusan Repovs
We study the topological structure of the direct limit $\glim G_n$ of a tower of topological groups in the category of topological groups and show that under some condition…