Abstract and concrete categories
Abstract and concrete categories
Fuzzy Sets and Systems - Special memorial volume on mathematical aspects of fuzzy set theory
Point-set lattice-theoretic topology
Fuzzy Sets and Systems - Special memorial volume on mathematical aspects of fuzzy set theory
An extensional treatment of lazy data flow deadlock
Selected papers of the workshop on Topology and completion in semantics
Continuity spaces: reconciling domains and metric spaces
MFPS '94 Proceedings of the tenth conference on Mathematical foundations of programming semantics
Fuzzy Relational Systems: Foundations and Principles
Fuzzy Relational Systems: Foundations and Principles
An enriched category approach to many valued topology
Fuzzy Sets and Systems
Theoretical Computer Science - Spatial representation: Discrete vs. continous computational models
Fuzzy sets and sheaves. Part I
Fuzzy Sets and Systems
A representation theorem for fuzzy pseudometrics
Fuzzy Sets and Systems
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For a GL-monoid L, Hohle introduced L-valued sets to formalize the mathematical theory of identity and existence in monoidal logic. For the purpose of analyzing deadlock situations in data flow networks, the notion of partial metric space was proposed by Matthews. Later on a lattice-theoretic generalization of (pseudo) partial metric spaces, extending the range of (pseudo) partial metrics to a value lattice V, were studied under the name of V-(pseudo) pmetric spaces. Referring to a GL-monoid L and a dual GL-monoid V, we show that L-valued sets are order-theoretically dual to V-pseudopmetric spaces, and apply this duality to the representation of V-pseudopmetric spaces and the determination of their various categorical properties. In addition to this, the present paper provides not only some new results about the representation of L-valued sets and their categories, but also some non-trivial categorical connections between L-valued sets and V-pseudopmetric spaces.