Strong one-sided density without uniform density

TL;DR

This paper presents examples distinguishing between different types of density properties in sets, showing that certain dense sets lack uniform density and vice versa, clarifying the relationship between these concepts.

Contribution

The paper provides explicit examples demonstrating that strong one-sided density does not imply uniform density, and that uniform density does not necessarily imply strong uniform density.

Findings

A closed, strongly one-sided dense set not of uniform density type.

A set of uniform density type not of strong uniform density type.

Abstract

In this paper we give an example of a closed, strongly one-sided dense set which is not of uniform density type. We also show that there is a set of uniform density type which is not of strong uniform density type.