Topological Finite-determinacy of Functions with Non-isolated Singularities
نویسنده
چکیده
We introduce the concept of topological finite-determinacy for germs analytic functions within a fixed ideal I, which provides a notion of topological finite-determinacy of functions with non-isolated singularities. We generalize classical results of Thom and Varchenko stating the following: let A be the complement in the ideal I of the space of germs whose topological type remains unchanged under a deformation within the ideal that only modifies sufficiently large order terms of the Taylor expansion; then A has infinite codimension in I in a suitable sense. We also prove the existence of generic topological types of families of germs of I parametrized by an irreducible analytic set.
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