Relationships between some selection principles and star selection principles

TL;DR

This paper explores the relationships between newly defined selection principles and classical star selection principles, answering open questions and establishing equivalences through collections of complements and refinements.

Contribution

It clarifies the connections between various selection principles and classical star principles, providing new equivalences and insights into their relationships.

Findings

Some selection principles are equivalent via collections of complements.

Other results involve collections of refinements.

The paper answers previously posed open questions.

Abstract

Motivated by the definition of classical star selection principles, Cruz-Castillo, Ram\'irez-P\'aramo and Tenorio defined some selection principles and posed several questions about relationships between these notions and some of the classical star selection principles. The main goal of this paper is to answer the questions posed by these authors. In addition, we show that some of these defined selection principles are equivalent by taking collections of complements; also, some other results are provided involving collections of refinements.