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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.

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