Bounding, splitting, and almost disjointness

TL;DR

This paper explores the relationships between key combinatorial cardinal characteristics of the continuum, focusing on bounding, splitting, and almost disjointness, and examines the existence of specific splitting families.

Contribution

It provides new insights into the connections between bounding, closed almost disjointness, and splitting numbers, and analyzes conditions for the existence of particular splitting families.

Findings

Established relationships between bounding and splitting numbers.

Identified conditions for the existence of certain splitting families.

Analyzed the impact of these properties on the structure of the continuum.

Abstract

We investigate some aspects of bounding, splitting, and almost disjointness. In particular, we investigate the relationship between the bounding number, the closed almost disjointness number, splitting number, and the existence of certain kinds of splitting families.