School of Mechanical Engineering, University of Applied Sciences Stralsund, D-18435 Stralsund, Germany
10.22111/ijfs.2020.5118
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.
Jäger, G. (2020). The Wijsman structure of a quantale-valued metric space. Iranian Journal of Fuzzy Systems, 17(1), 171-184. doi: 10.22111/ijfs.2020.5118
MLA
G. Jäger. "The Wijsman structure of a quantale-valued metric space". Iranian Journal of Fuzzy Systems, 17, 1, 2020, 171-184. doi: 10.22111/ijfs.2020.5118
HARVARD
Jäger, G. (2020). 'The Wijsman structure of a quantale-valued metric space', Iranian Journal of Fuzzy Systems, 17(1), pp. 171-184. doi: 10.22111/ijfs.2020.5118
VANCOUVER
Jäger, G. The Wijsman structure of a quantale-valued metric space. Iranian Journal of Fuzzy Systems, 2020; 17(1): 171-184. doi: 10.22111/ijfs.2020.5118
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