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QUANTALE-VALUED GAUGE SPACES | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 7، دوره 15، شماره 1، اردیبهشت 2018، صفحه 103-122 اصل مقاله (406.33 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2018.3581 | ||
| نویسندگان | ||
| Gunther Jager* 1؛ Wei Yao2 | ||
| 1University of Applied Sciences Stralsund, D-18435 Stralsund, Germany | ||
| 2Hebei University of Science and Technology, 050054 Shijiazhuang, P.R.China | ||
| چکیده | ||
| We introduce a quantale-valued generalization of approach spaces in terms of quantale-valued gauges. The resulting category is shown to be topological and to possess an initially dense object. Moreover we show that the category of quantale-valued approach spaces defined recently in terms of quantale-valued closures is a coreflective subcategory of our category and, for certain choices of the quantale, is even isomorphic to our category. Finally, the category of quantale-valued metric spaces is shown to be coreflectively embedded in our category. | ||
| کلیدواژهها | ||
| $L$-gauge space؛ $L$-approach space؛ $L$-metric space؛ Continuity space | ||
| مراجع | ||
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