Generalised filters 2

We continue the study, started in [8], of generalised filters. Prime prefil ters have played a central role in the theory of (Lowen) fuzzy uniform spac es and Lowen discovered a characterisation of the set of all minimal prime prefilters finer than a given prefilter in terms of ultrafilters. We define the notion of a prime generalised filter and describe the set of all minim al prime g-filters finer than a given g-filter in terms of ultrafilters. Th e relationship between prime prefilters and prime g-filters is revealed. Th e behaviour of the images and preimages of g-filters are investigated. (C) 1999 Elsevier Science B.V. All rights reserved.