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THE CATEGORY OF T-CONVERGENCE SPACES AND ITS CARTESIAN-CLOSEDNESS | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 9، دوره 14، شماره 3، شهریور 2017، صفحه 121-138 اصل مقاله (424.14 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2017.3259 | ||
| نویسندگان | ||
Qian Yu؛ Jinming Fang 
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| Department of Mathematics, Ocean University of China, 238 Songling Road, 266100, Qingdao, P.R. China | ||
| چکیده | ||
| In this paper, we define a kind of lattice-valued convergence spaces based on the notion of $\top$-filters, namely $\top$-convergence spaces, and show the category of $\top$-convergence spaces is Cartesian-closed. Further, in the lattice valued context of a complete $MV$-algebra, a close relation between the category of $\top$-convergence spaces and that of strong $L$-topological spaces is established. In details, we show that the category of strong $L$-topological spaces is concretely isomorphic to that of strong $L$-topological $\top$-convergence spaces categorically and bireflectively embedded in that of $\top$-convergence spaces. | ||
| کلیدواژه‌ها | ||
| T- lter؛ T-convergence؛ Cartesian-closedness؛ Topological category؛ Reflection؛ Strong L-topology | ||
| مراجع | ||
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