Characterizations of $L$-convex spaces

نویسندگان

  • Bin Pang Shenzhen Graduate School, Harbin Institute of Technology, 518055 Shen- zhen, P.R. China
  • Yi Zhao Shenzhen Graduate School, Harbin Institute of Technology, 518055 Shen- zhen, P.R. China
چکیده مقاله:

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.

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عنوان ژورنال

دوره 13  شماره 4

صفحات  51- 61

تاریخ انتشار 2016-08-30

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