Topologically principal part of analytic functions

Author:
Etsuo Yoshinaga

Journal:
Trans. Amer. Math. Soc. **314** (1989), 803-814

MSC:
Primary 58C27

DOI:
https://doi.org/10.1090/S0002-9947-1989-0930085-5

MathSciNet review:
930085

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Abstract: The problem of -sufficiency of jets is one of the most interesting problems in the theory of functions or singularities. Roughly speaking, it is the problem of determining a *topologically principal part* of the Taylor expansion of a given function at the origin of Euclidean space. Here, the topologically principal part should satisfy the properties that it is as small as possible a part of the Taylor expansion of and that the local topological type of at the origin is determined by it. If a function is an isolated singularity at the origin or has a nondegenerate Newton principal part (see (1.2)), then we know some answers to this problem (see (1.1), (1.3)). The purpose of this paper is to give some results for this problem for any analytic function. The main results are formulated in (1.5), (1.6), and (1.7).

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1989-0930085-5

Keywords:
Topologically principal part,
topological triviality,
nondegenerate Newton principal part

Article copyright:
© Copyright 1989
American Mathematical Society