Finite relative determination and relative stability

León Kushner and Brasil Terra Leme

Vol. 192 (2000), No. 2, 315–328

DOI: 10.2140/pjm.2000.192.315

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.

Milestones

Received: 16 June 1998

Revised: 19 October 1998

Published: 1 February 2000