%0 Journal Article
%T Characterizations of $L$-convex spaces
%J Iranian Journal of Fuzzy Systems
%I University of Sistan and Baluchestan
%Z 1735-0654
%A Pang, Bin
%A Zhao, Yi
%D 2016
%\ 08/30/2016
%V 13
%N 4
%P 51-61
%! Characterizations of $L$-convex spaces
%K $L$-convex structure
%K $L$-concave structure
%K Convex $L$-closure operator
%K Concave $L$-interior operator
%K Concave $L$-neighborhood system
%R 10.22111/ijfs.2016.2595
%X 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.
%U http://ijfs.usb.ac.ir/article_2595_892a5985091b412961eb99fb84c5bfbe.pdf