Skip to main content
eScholarship
Open Access Publications from the University of California

The fixed-point theory of strictly contracting functions on generalized ultrametric semilattices

  • Author(s): Matsikoudis, E
  • Lee, EA
  • et al.
Abstract

© E. Matsikoudis & E. A. Lee. 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.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Main Content
Current View