The Wijsman structure of a quantale-valued metric space

Document Type : Research Paper

Author

School of Mechanical Engineering, University of Applied Sciences Stralsund, D-18435 Stralsund, Germany

Abstract

We define and study a quantale-valued Wijsman structure on the hyperspace of all non-empty closed sets of a quantale-valued metric space. We show its admissibility and that the metrical coreflection coincides with the quantale-valued Hausdorff metric and that, for a metric space, the topological coreflection coincides with the classical Wijsman topology. We further define an index of compactness and show that the indices of compactness of the quantale-valued metric space and of the hyperspaces equipped with the quantale-valued Hausdorff metric and with the quantale-valued Wijsman structure coincide.

Keywords

Iranian Journal of Fuzzy Systems
Volume 17, Issue 1
January and February 2020
Pages 171-184

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