L-convex convergence relation and L-convex ideal-convergence structure

In the framework of L-convex spaces, this paper is aim to study fuzzy convergence structuresof L-convex space in a viewpoint of fuzzy relations. For this purpose, L-directed relation is introducedand some of its examples are proposed. Based on this, notions of L-convergence relation and L-convex convergence relation are introduced. It is proved that there is a Galois's connection between the category of L-convergence relation spaces and the category of L-convex enclosed relation spaces. In particular, L-convex convergence relation spaces and L-convex enclosed relation spaces are categorically isomorphic. Also, notions of L-ideal-convergence structure and L-convex ideal-convergence structure are introduced. It is proved that L-convergence relation spaces and L-ideal-convergence spaces are categorically isomorphic. In particular, L-convex convergence relation spaces and L-convex ideal-convergence spaces are categorically isomorphic.

کلیدواژه ها:

L-convex space ، L-directed relation ، L-convergence relation ، L-convex convergence relation ، L- ideal-convergence structure ، L-convex ideal convergence structure