Abstract

This paper is divided in three parts. The first part deals with the equivalence of finite determination on the right and finite relative determination (with respect to S) under some conditions on S. The second part deals with infinite determinacy (with respect to S, a germ of a closed set of Rⁿ). Both generalize results of P. Porto [On relative stability of function germs, Bol. Soc. Bras. Mat., 14(2) (1983), 99–108.] for a big family of closed subsets S of Rⁿ. The third part is a special case which is quite interesting, when S coincides with the closure of its interior.

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