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arXiv · 1309.0894

The Fixed-Point Theory of Strictly Contracting Functions on Generalized Ultrametric Semilattices

Eleftherios Matsikoudis·Edward A. Lee
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Abstract

We introduce a new class of abstract structures, which we call generalized ultrametric semilattices, and in which the meet operation of the semilattice coexists with a generalized distance function in a tightly coordinated way. We prove a constructive fixed-point theorem for strictly contracting functions on directed-complete generalized ultrametric semilattices, and introduce a corresponding induction principle. We cite examples of application in the semantics of logic programming and timed computation, where, until now, the only tool available has been the non-constructive fixed-point theorem of Priess-Crampe and Ribenboim for strictly contracting functions on spherically complete generalized ultrametric semilattices.

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Eleftherios Matsikoudis, Edward A. Lee. 2013-09-04. The Fixed-Point Theory of Strictly Contracting Functions on Generalized Ultrametric Semilattices. https://doi.org/10.4204/eptcs.126.5

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