FUZZY PROXIMITIES INDUCED BY FUNCTIONAL FUZZY SEPARATION

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 Cech fuzzy proximity of an N-completely regular fns (X, rho). We establish that it is the finest fuzzy proximity that induces the fns (X, rho). We study in some detail the Czech fuzzy proximities obtained from N-normal fns's.