L-CONVEX SYSTEMS an‎d THE CATEGORICAL ISOMORPHISM TO SCOTT-HULL OPERATORS

The concepts of L-convex systems and Scott-hull spaces are pro- posed on frame-valued setting. Also, we establish the categorical isomorphism between L-convex systems and Scott-hull spaces. Moreover, it is proved that the category of L-convex structures is bire ective in the category of L-convex systems. Furthermore, the quotient systems of L-convex systems are studied.