The Wijsman structure of a quantale-valued metric space

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JAGER G.

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Journal: Iranian Journal of Fuzzy Systems Year:2020 | Volume:17 | Issue:1 Page(s): 171-184

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Information Journal Paper

Title

The Wijsman structure of a quantale-valued metric space

Author(s)

JAGER G. | Issue Writer Certificate

Keywords

L-gauge spaceQ2

L-metric spaceQ2

L-Hausdorff metricQ2

L-hyperspaceQ2

Wijsman topologyQ2

Abstract

We define and study a quantale-valued Wijsman structure on the hyperspace of all non-empty closed sets of a quantalevalued 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.

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APA: Copy

JAGER, G.. (2020). The Wijsman structure of a quantale-valued metric space. IRANIAN JOURNAL OF FUZZY SYSTEMS, 17(1 ), 171-184. SID. https://sid.ir/paper/374736/en

Vancouver: Copy

JAGER G.. The Wijsman structure of a quantale-valued metric space. IRANIAN JOURNAL OF FUZZY SYSTEMS[Internet]. 2020;17(1 ):171-184. Available from: https://sid.ir/paper/374736/en

IEEE: Copy

G. JAGER, “The Wijsman structure of a quantale-valued metric space,” IRANIAN JOURNAL OF FUZZY SYSTEMS, vol. 17, no. 1 , pp. 171–184, 2020, [Online]. Available: https://sid.ir/paper/374736/en

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