From homogeneity to discrete homogeneity

TL;DR

This survey reviews classical and recent results on various types of homogeneity in topology, introduces new findings, and discusses open problems related to n-homogeneity, discrete homogeneity, and countable dense homogeneity.

Contribution

It provides a comprehensive overview of homogeneity types and presents new results and open problems in the field.

Findings

New results on homogeneity types are presented.

Several open problems are posed for future research.

The survey synthesizes classical and recent developments in the area.

Abstract

This is a survey of recent and classical results concerning various types of homogeneity, such as n-homogeneity, discrete homogeneity, and countable dense homogeneity. Some new results are also presented, and several problems are posed.