A non-commutative approach to uniform structures
Kamal El-Saady · Journal of Intelligent & Fuzzy Systems · 2016
This paper presents a theory of uniform-type structures in the non-commutative sense. The theory comprises the theory of covering-uniformities for quantales as a generalization of the classical theory of covering-uniformities for frames. Also, by introducing quantale-valued covers of a set, we pres ent a general framework for uniform structures on very general L-valued spaces (for L a quantale). The categories of (covering) uniform quantales and L-valued uniform spaces here introduced and the adjunction between them is studied.