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Lubica Hola

Publications and source records attributed to Lubica Hola.

7 recordsLinked to original sources
arXiv2023

Properties of equi-Baire 1 and equi-Lebesgue families of functions

We study several properties of equi-Baire 1 families of functions between metric spaces. We consider the related equi-Lebesgue property for such families. We examine the behaviour of equi-Baire 1 and equi-Lebesgue families with respect to pointwise and uniform convergence. In particular, we obtain a criterion for a choice of a uniformly convergent subsequence from a sequence of functions that form an equi-Baire 1 family, which solves a problem posed in [3]. Finally, we discuss the notion of equi-cliquishness and relations between equi-Baire 1 families and sets of equi-continuity points.

math.GN↗
arXiv2015

Embeddings in the Fell and Wijsman topologies

It is shown that if a $T_2$ topological space $X$ contains a closed uncountable discrete subspace, then the spaces $(ω_1 + 1)^ω$ and $(ω_1 + 1)^{ω_1}$ embed into $(CL(X),τ_F)$, the hyperspace of nonempty closed subsets of $X$ equipped with the Fell topology. If $(X,d)$ is a non-separable perfect topological space, then $(ω_1 + 1)^ω$ and $(ω_1 + 1)^{ω_1}$ embed into $(CL(X),τ_{w(d)})$, the hyperspace of nonempty closed subsets of $X$ equipped with the Wijsman topology, giving a partial answer to the Question 3.4 in [CJ].

math.GN↗
arXiv2014

An embedding in the Fell topology

It is shown that if a $T_2$ topological space contains an uncountable closed discrete set, then $ω_1 \times (ω_1 + 1)$ embeds as a closed subspace of $(CL(X),τ_F)$, the hyperspace of nonempty closed subsets of $X$ equipped with the Fell topology.

math.GN↗