FUZZY PROXIMITIES INDUCED BY FUNCTIONAL FUZZY SEPARATION

Mashhour and Morsi introduced an axiom of N-complete regularity to cha racterize the Lowen fuzzy uniformizable fuzzy neighbourhood spaces (fn s's). Guided by that axiom we supply a Sierpinski object for the Artic o-Moresco category FP of fuzzy proximity spaces, which Katsaras has sh own to be a topological category. We define the degree of functional f uzzy separatedness of a pair of subsets of a fns. We use that notion t o define the Cech fuzzy proximity of an N-completely regular fns (X, r ho). We establish that it is the finest fuzzy proximity that induces t he fns (X, rho). We study in some detail the Czech fuzzy proximities o btained from N-normal fns's.