A Note on the Hausdorff Number of Compact Topological Spaces

TL;DR

This paper explores the Hausdorff number in topological spaces, analyzing its relationship with compactness to deepen understanding of topological properties and their implications.

Contribution

It provides a topological perspective on the Hausdorff number and investigates its connections with compactness, offering new insights into their interplay.

Findings

Hausdorff number relates to compactness in specific ways

Generalizations of bounds for cardinality are discussed

Topological properties influenced by Hausdorff number are examined

Abstract

The notion of Hausdorff number of a topological space is first introduced in \cite{bonan}, with the main objective of using this notion to obtain generalizations of some known bounds for cardinality of topological spaces. Here we consider this notion from a topological point of view and examine interrelations of the Hausdorff number with compactness.