Abstract and concrete categories
Abstract and concrete categories
Fuzzy Sets and Systems
On level-topologies and maximality of fuzzy topological spaces
Fuzzy Sets and Systems
Fuzzy uniform structures and continuous t-norms
Fuzzy Sets and Systems
On lattice-valued frames: The completely distributive case
Fuzzy Sets and Systems
On the uniformization of lattice-valued frames
Fuzzy Sets and Systems
| Hi-index | 0.20 |
By introducing lattice-valued covers of a set, we present a general framework for uniform structures on very general L-valued spaces (for L an integral commutative quantale). By showing, via an intermediate L-valued structure of uniformity, how filters of covers may describe the uniform operators of Hutton, we prove that, when restricted to Girard quantales, this general framework captures a significant class of Hutton's uniform spaces. The categories of L-valued uniform spaces and L-valued uniform frames here introduced provide (in the case L is a complete chain) the missing vertices in the commutative cube formed by the classical categories of topological and uniform spaces and their corresponding pointfree counterparts (forming the base of the cube) and the corresponding L-valued categories (forming the top of the cube).