L-contiguities and their order structure

The present paper introduces L-contiguity and L-merotopy and presents a unified study of L-proximity, L-contiguity and L-merotopy on a set X. Corresponding to each L-contiguity there is an L-merotopy which is contigual, if this L-contiguity is obtained by restricting the cardinality of a given L-merotopy, then the two L-merotopies in hand are the same. It is shown that the family of all L-contiguities and the family of all L-contiguities, which induce a given L-proximity, form complete distributive lattices.