Further study on induced L-convex spaces

Abstract

In this paper, the relationship 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 relationship of them are investigated.