A COMMON IMPROVEMENT OF FUZZY TOPOLOGICAL SPACES AND FUZZY (QUASI) UNIFORM SPACES

Abstract

Using fuzzy filters in the sense of P. Eklund and W. Gähler [2], it turns out that fuzzy preuniform convergence spaces introduced in [11] form a strong topological universe in which fuzzy topological spaces as well as fuzzy (quasi) uniform spaces can be studied. Thus, better tools such as the existence of natural function spaces, the existence of one-point extensions (and consequently, the hereditariness of quotient maps), and the productivity of quotient maps are available.