arXiv subjects

Jaroslav Šupina

Publications and source records attributed to Jaroslav Šupina.

5 recordsLinked to original sources

arXiv2026

The Higher Closed Null Ideal(s)

We generalise the $σ$-ideal $\mathcal E$ generated by the closed Lebesgue null subsets of the Cantor space ${}^ω2$ to the context of higher Cantor spaces ${}^κ2$ for an uncountable cardinal $κ$ satisfying $κ=κ^{<κ}$. We introduce candidates for a higher closed null ideal based on slaloms on partitions of $κ$ into sets of size ${<}κ$, and study their combinatorial properties. We also give some relations between the cardinal characteristics of the higher closed null ideals and other cardinal characteristics.

math.LO↗

arXiv2026

New approaches to remote points

For a given Tychonoff space $X$, a point $p\in β(X)\setminus X$ is called {\em remote} if $p$ is not in the closure of any nowhere dense subset of $X$. In this paper, we characterize spaces with remote points in terms of certain topological ultrafilters, measures, and compact-like properties corresponding to the ideal consisting of nowhere dense sets. It is shown that the space of remote points is homeomorphic to a subspace of the Stone space taken over the smallest Boolean algebra containing all open and nowhere dense sets. Also, we show that the space of remote points of $\mathbb R$ is $ω$-bounded.

math.GN↗

arXiv2024

Local and global properties of spaces of minimal usco maps

In this paper, we study an interplay between local and global properties of spaces of minimal usco maps equipped with the topology of uniform convergence on compact sets. In particular, for each locally compact space $X$ and metric space $Y$, we characterize the space of minimal usco maps from $X$ to $Y$, satisfying one of the following properties: (i) compact, (ii) locally compact, (iii) $σ$-compact, (iv) locally $σ$-compact, (v) metrizable, (vi) ccc, (vii) locally ccc, where in the last two items we additionally assumed that $Y$ is separable and non-discrete. Some of the aforementioned results complement ones of Ľubica Holá and Dušan Holý. Also, we obtain analogical characterizations for spaces of minimal cusco maps.

math.GN↗

arXiv2023

Conditional Aggregation-Based Choquet Integral as a Choquet Integral on a Hyperspace

We aim at representing the recently introduced conditional aggregation-based Choquet integral as a standard Choquet integral on a hyperset. The representation is one of transformations considered by R.R. Yager and R. Mesiar in 2015. Thus we study the properties of the conditional aggregation-based Choquet integral using well-known facts about the standard Choquet integral. In particular, we obtain several formulas for its computation. We also provide the representation of the conditional aggregation-based Choquet integral in terms of the Möbius transform.

math.FA↗

arXiv2023

Conditional aggregation-based Choquet integral on discrete space

We derive computational formulas for the generalized Choquet integral based on the novel survival function introduced by M. Boczek et al. [1]. We demonstrate its usefulness on the Knapsack problem and the problem of accommodation options. Moreover, we describe sufficient and necessary conditions under which novel survival functions based on different parameters coincide. This is closely related to the incomparability of input vectors (alternatives) in decision-making processes.

math.OC↗