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Journal Articles Cahiers de topologie et géométrie différentielle catégoriques Year : 2023

A logical analysis of fixpoint theorems

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.

Dates and versions

hal-04025858 , version 1 (13-03-2023)

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Arij Benkhadra, Isar Stubbe. A logical analysis of fixpoint theorems. Cahiers de topologie et géométrie différentielle catégoriques, 2023, LXIV (1), pp.97--121. ⟨hal-04025858⟩
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