In this and a subsequent paper, using the notion of fuzzy neighborhood filter which has been
defined in , we introduce and study the separation axioms Ti, i = 0; 1; 2; 3; 4 in the case of a fuzzy
topology. These axioms are related only to usual points and ordinary subsets. In the classical case
L = f0; 1g these axioms are the usual ones. These axioms fulfills many properties analogous to
the usual axioms. Whereas this paper is devoted to the axioms T0; T1; T2, in part II the axioms
T3; T4 are introduced and studied.
Keywords: Fuzzy filters, Principal fuzzy filters, Fuzzy neighborhood filters, Valued fuzzy neighborhoods,
Fuzzy topologies, Fuzzy separation axioms