Abstract
Mashhour and Morsi introduced an axiom of N-complete regularity to characterize the Lowen fuzzy uniformizable fuzzy neighbourhood spaces (fns's). Guided by that axiom we supply a Sierpinski object for the Artico-Moresco category FP of fuzzy proximity spaces, which Katsaras has shown to be a topological category. We define the degree of functional fuzzy separatedness of a pair of subsets of a fns. We use that notion to define the Čech fuzzy proximity of an N-completely regular fns ( X, ϱ). We establish that it is the finest fuzzy proximity that induces the fns ( X, ϱ). We study in some detail the Čech fuzzy proximities obtained from N-normal fns's.
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