On expand-contract plasticity in quasi-metric spaces

TL;DR

This paper investigates the expand-contract property in quasi-metric spaces, revealing differences from metric spaces and establishing conditions where the property holds.

Contribution

It demonstrates that the expand-contract property does not generally hold in quasi-metric spaces and provides conditions under which it does.

Findings

The property fails in general for quasi-metric spaces.

Certain conditions ensure the property holds in hereditarily precompact quasi-metric spaces.

Abstract

It is known that if any function acting from precompact metric space to itself increases the distance between some pair of points then it must decrease distance between some other pair of points. We show that this is not the case for quasi-metric spaces. After that, we present some sufficient conditions under which the previous property holds true for hereditarily precompact quasi-metric spaces.