Characterizations of L-order L-convex spaces

Document Type : Research Paper


1 School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Songjiang 201620, China

2 School of Mathematics, Hunan University, Changsha 410082, China

3 Fuzhou Teachers' College, East China University of Technology, Fuzhou 344000, China



In this paper, the concepts of $L$-enclosed $L$-order space, $L$-order $L$-concave space, $L$-internal $L$-order space and $L$-order $L$-convex filter are introduced. The main results are:
(1) the categories of $L$-order $L$-convex spaces, $L$-enclosed $L$-order spaces, $L$-order $L$-concave spaces and $L$-internal $L$-order spaces are isomorphic; (2) the category of $L$-order convergence spaces based on $L$-order $L$-convex filters is topological; (3) there is a Galois correspondence between the category of $L$-order convergence spaces and that of $L$-order $L$-convex spaces.