A semifilter approach to selection principles

TL;DR

This paper introduces a semifilter approach to classical covering properties, establishing new bounds and conditions for Menger and Hurewicz properties in topological spaces and subsets of the real line.

Contribution

It develops the semifilter framework for Menger and Hurewicz properties, linking small cardinals to additivity numbers and property implications.

Findings

g is a lower bound for the additivity of Menger subspaces

Under u<g, certain subsets of the real line are Hurewicz

The semifilter approach connects cardinal invariants with covering properties

Abstract

We develop the semifilter approach to the classical Menger and Hurewicz covering properties and show that the small cardinal g is a lower bound of the additivity number of the family of Menger subspaces of the Baire space, and under u< g every subset X of the real line with the property Split(Lambda,Lambda) is Hurewicz.