Characterizations of L-convex spaces

In this paper, the concepts of L-concave structures, concave L-interior operators and concave L-neighborhood systems are introduced. It is shown that the category of L-concave spaces and the category of concave L-interior spaces are isomorphic, and they are both isomorphic to the category of concave L-neighborhood systems whenever L is a completely distributive lattice. Also, it is proved that these categories are all isomorphic to the category of L-convex spaces whenever L is a completely distributive lattice with an order-reversing involution operator.

کلیدواژه ها:

L-convex structure ، L-concave structure ، Convex L-closure operator ، Concave L-interior operator ، Concave L-neighborhood system