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The metric closure powerspace construction

  • Robert E. Kent
Part II Structure Theory Of Continuous Posets And Related Objects
Part of the Lecture Notes in Computer Science book series (LNCS, volume 298)

Abstract

In this paper we develop a natural powerobject construction in the context of enriched categories, a context which generalizes the traditional order-theoretic and metric space contexts. This powerobject construction is a subobject transformer involving the dialectical flow of closed subobjects of enriched categories. It is defined via factorization of a comprehension schema over metrical predicates, followed by the fibrational inverse image of metrical predicates along character, the left adjoint in the comprehension schema. A fundamental continuity property of this metrical powerobject construction vis-a-vis greatest fixpoints is established by showing that it preserves the limit of any Cauchy ωop-diagram. Using this powerobject construction we unify two well-known fixpoint semantics for concurrent interacting processes.

Keywords

Inverse Image Normed Category Comprehension Schema Enrich Category Adjoint Pair 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Robert E. Kent
    • 1
  1. 1.Department of Electrical Engineering and Computer ScienceUniversity of Illinois at ChicagoChicago

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