Complete ξ-grills and (L,n)-merotopies

The present paper introduces the concepts of a complete ξ-grill, a concept similar to that of a bunch in classical theory, and of an L-merotopy. The study of the order structure as well as the topological structure on the family of all complete ξ-grills on an L-merotopic space (LX,ξ) is undertaken; corresponding to each L-Čech closure operator on a set X, an L-merotopy on X is obtained. An (L,n)-merotopy on X is also introduced and studied.