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arXiv · 2211.01782

A logical analysis of fixpoint theorems

Arij Benkhadra·Isar Stubbe
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Abstract

We prove a fixpoint theorem for contractions on Cauchy-complete quantale-enriched categories. It holds for any quantale whose underlying lattice is continuous, and applies to contractions whose control function is sequentially lower-semicontinuous. Sufficient conditions for the uniqueness of the fixpoint are established. Examples include known and new fixpoint theorems for metric spaces, fuzzy metric spaces, and probabilistic metric spaces.

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Arij Benkhadra, Isar Stubbe. 2022-11-03. A logical analysis of fixpoint theorems. https://arxiv.org/abs/2211.01782

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