PRE-WEIGHTED HOMOGENEOUS MAP GERMS FINITE DETERMINACY AND TOPOLOGICALTRIVIALITY

In this paper we introduce the notion of G-pre-weighted homogeneous ma p germ, (G is one of Mather's groups A or K) and show that any G-pre-w eighted homogeneous map germ is G- finitely determined. We also give a n explicit ''order'', based on;the Newton polyhedron of a pre-weighted homogeneous germ of function, such that the topological structure is preserved after perturbations by terms of higher order.