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Characterizations of $L$-convex spaces | ||
Iranian Journal of Fuzzy Systems | ||
مقاله 5، دوره 13، شماره 4، پاییز 2016، صفحه 51-61 اصل مقاله (345.73 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22111/ijfs.2016.2595 | ||
نویسندگان | ||
Bin Pang؛ Yi Zhao ![]() | ||
Shenzhen Graduate School, Harbin Institute of Technology, 518055 Shen- zhen, P.R. China | ||
چکیده | ||
In this paper, the concepts of $L$-concave structures, concave $L$-interior operators and concave $L$-neighborhood systems are introduced. It is shown that the category of $L$-concave spaces and the category of concave $L$-interior spaces are isomorphic, and they are both isomorphic to the category of concave $L$-neighborhood systems whenever $L$ is a completely distributive lattice. Also, it is proved that these categories are all isomorphic to the category of $L$-convex spaces whenever $L$ is a completely distributive lattice with an order-reversing involution operator. | ||
کلیدواژهها | ||
$L$-convex structure؛ $L$-concave structure؛ Convex $L$-closure operator؛ Concave $L$-interior operator؛ Concave $L$-neighborhood system | ||
مراجع | ||
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