Variations of star selection principles on Hyperspaces

TL;DR

This paper explores how different star selection principles, including selective and absolute versions, apply to hyperspaces with various topologies, providing new characterizations of their properties.

Contribution

It introduces combinatorial principles that characterize hyperspaces satisfying variations of classical star selection principles, extending understanding of hyperspace topologies.

Findings

Characterization of hyperspaces with star selection principles

Analysis of hyperspaces with Fell and Vietoris topologies

Extension of classical principles to hyperspace contexts

Abstract

In this paper we define some combinatorial principles to characterize spaces $X$ whose hyperspace satisfies some variation of some classical star selection principle. Specifically, the variations characterized are the selective and absolute versions of the star selection principles for the Menger and Rothberger cases; also, the hyperspaces considered in these characterizations are $CL(X)$, $\mathbb{K}(X)$, $\mathbb{F}(X)$ and $\mathbb{CS}(X)$ in both cases, endowed with either the Fell topology or the Vietoris topology.