Relative S-C～0 Sufficiency And Relative S-V Sufficiency Of Jets Of Function Germs

It is more and more important that the studying of the relativity problems, since the development of singularity theory and the need of actual problems. Relative mapping is more particular than usual mapping. If we look for relative set S rationally, relative mapping can satisfy some conditions that usual mapping doesn't satisfy. We combine the basic theory of relative mapping and classical singularity theory and C~0 sufficiency, generalize C~0 sufficiency and V sufficiency.There are two chapers in this paper. Chapter one includes some basic definitions and theorems such as C~0 sufficiency, relative mapping and so on. Chapter two includes the main results in this paper, theorem 2.2.1 and theorem 2.2.2 and some lemmas that are needed by the proofs of these theorems.