Bin Pang - Shenzhen Graduate School, Harbin Institute of Technology, ۵۱۸۰۵۵ Shen- zhen, P.R. China
Yi Zhao - Shenzhen Graduate School, Harbin Institute of Technology, ۵۱۸۰۵۵ Shen- zhen, P.R. China

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.

L-convex structure, L-concave structure, Convex L-closure operator, Concave L-interior operator, Concave L-neighborhood system