Fuzzy topological spaces

(1) We define normality for fuzzy topological spaces, define a fuzzy unit interval, and prove a Urysohn type lemma. (2) We define uniformities on fuzzy lattices, and characterise uniformizability in terms of complete regularity. (3) We define the product of a collection of fuzzy topological spaces. We define compactness and connectedness, and show that the product is compact (connected) iff each factor space is. (4) We place normality and complete regularity within a coherent hierarchy of separation and regularity axioms. We prove the usual implications, and the usual theorems about compactness and products. (5) We give alternative definitions of uniformities and pseudometrics, and show a compact R1 space has a unique uniformity