A converse of the Banach contraction principle for partial metric spaces and the continuum hypothesis

TL;DR

This paper presents a version of the inverse Banach contraction principle tailored for partial metric spaces and establishes its equivalence to the continuum hypothesis, linking fixed point theory with set-theoretic assumptions.

Contribution

It introduces a novel inverse contraction principle for partial metric spaces and proves its equivalence to the continuum hypothesis, connecting fixed point theory with foundational set theory.

Findings

New inverse contraction principle for partial metric spaces

Equivalence between the principle and the continuum hypothesis

Bridges fixed point theory with set-theoretic hypotheses

Abstract

A version of the Bessaga inverse of the Banach contraction principle for partial metric spaces is presented. Equivalence of that version and the continuum hypothesis is shown as well.