Characterizations of L-order L-convex spaces

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:(۱) 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; (۲) the category of L-order convergence spaces based on L-order L-convex filters is topological; (۳) there is a Galois correspondence between the category of L-order convergence spaces and that of L-order L-convex spaces.

Keywords:

L-order L-convexity , L-enclosed L-order , L-order L-convex filter , L-order L-concavity , L-order convergence structure