In this paper, the relationships of induced L-convex spaces with L-hull operators, product spaces, and quotient spaces are discussed. It is shown that the quotient L-convex structure of induced L-convex structure is exactly the induced L-convex structure by quotient convex structure. Moreover, sub-S 1 , sub-S 2 , S 2 and S 3 separation axioms are introduced in L-convex spaces and induced L-convex spaces. Some properties and relationships of them are investigated