Topological types of finitely-𝐶⁰-𝐾-determined map-germs

Nishimura, Takashi

doi:10.1090/S0002-9947-1989-0946220-9

Topological types of finitely-$C^ 0$-$K$-determined map-germs
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Trans. Amer. Math. Soc. 312 (1989), 621-639 Request permission

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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