Non-expansive bijections, uniformities and polyhedral faces

TL;DR

This paper generalizes the concept of expand-contract plasticity from strictly convex Banach spaces to spaces with polyhedral unit balls and further extends the notion to uniform spaces, broadening its applicability.

Contribution

It introduces a generalized framework for expand-contract plasticity applicable to a wider class of spaces, including uniform spaces and those with polyhedral unit balls.

Findings

Extended expand-contract plasticity to spaces with polyhedral extreme subsets.

Generalized expand-contract plasticity to uniform spaces.

Broadened the scope of plasticity results to more general metric spaces.

Abstract

We extend the result of B. Cascales at al. about expand-contract plasticity of the unit ball of strictly convex Banach space to those spaces whose unit ball is the union of all its finite-dimensional polyhedral extreme subsets. We also extend the definition of expand-contract plasticity to uniform spaces and generalize the theorem on expand-contract plasticity of totally bounded metric spaces to this new setting.