Diagonalizations of dense families

TL;DR

This paper introduces a unified framework for analyzing diagonalization properties of dense families in topological spaces, providing a comprehensive classification that consolidates existing methods and introduces new results.

Contribution

It offers the first complete classification of diagonalization properties of dense families in topological spaces, integrating various approaches and novel findings.

Findings

Complete classification of diagonalization properties

Integration of existing methods and new results

Enhanced understanding of dense family properties in topology

Abstract

We develop a unified framework for the study of properties involving diagonalizations of dense families in topological spaces. We provide complete classification of these properties. Our classification draws upon a large number of methods and constructions scattered in the literature, and on some novel results concerning the classical properties.