A common generalization of metric, ultrametric and topological fixed point theorems - alternative version

TL;DR

This paper introduces a unified fixed point theorem that generalizes and encompasses Banach's, ultrametric, and topological fixed point theorems, applicable in minimal, metric-free settings.

Contribution

It presents a new, broad fixed point theorem unifying various classical theorems without relying on metrics, applicable to diverse mathematical structures.

Findings

Unified fixed point theorem applicable to multiple contexts

Demonstrated applications to metric, ultrametric, and topological cases

Extended applicability to ordered abelian groups and fields

Abstract

We present a general fixed point theorem which can be seen as the quintessence of the principles of proof for Banach's Fixed Point Theorem, ultrametric and certain topological fixed point theorems. It works in a minimal setting, not involving any metrics. We demonstrate its applications to the metric, ultrametric and topological cases, and to ordered abelian groups and fields.