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The Wijsman structure of a quantale-valued metric space | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 13، دوره 17، شماره 1، فروردین و اردیبهشت 2020، صفحه 171-184 اصل مقاله (212.08 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2020.5118 | ||
| نویسنده | ||
| G. Jäger* | ||
| School of Mechanical Engineering, University of Applied Sciences Stralsund, D-18435 Stralsund, Germany | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| L-gauge space؛ L-metric space؛ L-Hausdorff metric؛ L-hyperspace؛ Wijsman topology | ||
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آمار تعداد مشاهده مقاله: 106 تعداد دریافت فایل اصل مقاله: 115 |
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