L-fuzzy syntopogenous structures, Part Ⅰ: Fundamentals and application to L-fuzzy topologies, L-fuzzy proximities and L-fuzzy uniformities

摘要

We introduce the concept of an L-fuzzy syntopogenous structure where L is a complete lattice endowed with an implicator → : L×L → L satisfying certain properties (in particular, as L one can take an MV-algebra). As special cases our L-fuzzy syntopogenous structures contain classical Csaszar syntopogenous structures, Katsaras-Petalas fuzzy syntopogenous structures as well as fuzzy syntopogeneous structures introduced in the previous work of the second named author (A. Sostak, Fuzzy syntopogenous structures. Quaest. Math. 20 (1997) 431-461). Basic properties of the category of L-fuzzy syntopogenous spaces are studied; categories of L-fuzzy topological spaces, L-fuzzy proximity spaces and L-fuzzy uniform spaces are characterized in the framework of the category of L-fuzzy syntopogenous spaces.