Abstract

We continue the study, started in [8], of generalised filters. Prime prefilters have played a central role in the theory of (Lowen) fuzzy uniform spaces 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 minimal prime g-filters finer than a given g-filter in terms of ultrafilters. The relationship between prime prefilters and prime g-filters is revealed. The behaviour of the images and preimages of g-filters are investigated.

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