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

摘要

The present paper introduces the concepts of a complete ζ-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 ζ-grills on an L-merotopic space (L~X, ζ) is undertaken; corresponding to each L-Cech closure operator on a set X, an L-merotopy on X is obtained. An (L, n)-merotopy on X is also introduced and studied.