Separation Axioms: Extension of Mappings And Embedding of Spaces

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.)

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