L-topological-convex spaces generated by L-convex bases

Abstract

In this paper, axiomatic definitions of both L-convex bases and L-convex subbases are introduced and their relations with L-convex spaces are studied. Based on this, the notion of L-topological-convex space is introduced as a triple (X, 𝓣, 𝓒), where X is a nonempty set, 𝓒 is an L-convex structure on X and 𝓣 is an L-cotopology on X compatible with 𝓒. It can be characterized by many means.

Keywords

• l-convex space
• l-convex enclose relation space
• l-topological-convex space
• l-topological-convex enclosed relation space
• 54a40
• 52a01