An axiomatic approach to bases and subbases in L-convex spaces and their applications

Considering a continuous lattice L as the lattice background, an axiomatic approach to bases and subbases in the framework of L-convex spaces is provided. Firstly, the concepts of bases and subbases in L-convex spaces are introduced and then L-convexity base axioms and L-convexity subbase axioms are proposed by abstracting the properties of bases and subbases, respectively. Secondly, some applications of L-convexity base axioms and L-convexity subbase axioms are investigated. It is shown that L-convexity base axioms can be used to demonstrate some relationship between spatial structures with respect to L-convex structures and L-convexity subbase axioms can be applied to define the join space and the product space of L-convex spaces.