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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Topological types of finitely-$ C\sp 0$-$ K$-determined map-germs

Author: Takashi Nishimura
Journal: Trans. Amer. Math. Soc. 312 (1989), 621-639
MSC: Primary 58C27
MathSciNet review: 946220
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Abstract: In this article, we investigate the following two problems

Problem 1. Is finite- $ {C^0}{\text{-}}K$-determinacy a topological invariant among analytic map-germs?

Problem 2. Do the topological types of all finitely- $ {C^0}{\text{-}}K$-determined map-germs have topological moduli, i.e. do they have infinitely many topological types with the cardinal number of continuum?

Problem $ 1$ is solved affirmatively in the complex case. Problem $ 2$ is solved negatively in the complex case; and affirmatively in the real case.

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Keywords: $ {C^0}{\text{-}}K$-determined map-germs, $ {C^0}{\text{-}}A$-equivalent, topological types
Article copyright: © Copyright 1989 American Mathematical Society