Chapter 6 investigates the important role of separation axioms in lattice-valued topology from the perspective of space embedding and mapping extension problems, while Chapter 7 examines separation axioms from the perspective of Stone-Cech-compactification and Stone-representation theorems.
1. Many-valued logic and fuzzy set theory.- 2. Powerset operator foundations for poslat fuzzy set theories and topologies.- Introductory notes to Chapter 3.- 3. Axiomatic foundations of fixed-basis fuzzy topology.- 4. Categorical foundations of variable-basis fuzzy topology.- 5. Characterization of L-topologies by L-valued neighborhoods.- 6. Separation axioms: Extension of mappings and embedding of spaces.- 7. Separation axioms: Representation theorems, compactness, and compactifications.- 8. Uniform spaces.- 9. Extensions of uniform space notions.- 10. Fuzzy real lines and dual real lines as poslat topological, uniform, and metric ordered semirings with unity.- 11. Fundamentals of generalized measure theory.- 12. On conditioning operators.- 13. Applications of decomposable measures.- 14. Fuzzy random variables revisited.