Formulations of L -convex hulls on some algebraic structures

Abstract

With a complete Heyting algebra L as the truth value table, we introduce L-ordered convex spaces, L-semilattice convex spaces, L-lattice convex spaces and L-standard convex spaces. These kinds of structures can be extracted from posets, semilattices, lattices and vector spaces. Above all, we obtain their corresponding L-convex hull formulae and analyze their corresponding L-convexity-preserving (resp., L-convex-to-convex) mappings.