Separation Axioms: Extension of Mappings And Embedding of Spaces

Abstract

The present chapter is intended to give a self-contained development of some of the topics of fuzzy topology (54A40) that involve L-real-valued continuous functions on L-topological spaces. The four major themes include separation of L-sets by continuous L-real functions, insertion of continuous L-real functions between two comparable L-real functions, extension of continuous L-real functions from a subspace to the entire space and embedding L-topological spaces into products. (In actual fact, it is the embedding of L-Tychonoff spaces into L-cubes which falls into that category of results.)KeywordsComplete LatticeExtension TheoremContinuous ExtensionRegular FamilySeparation AxiomThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.