2016
DOI: 10.4064/ap3835-5-2016
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Finite determinacy of non-isolated singularities

Abstract: We give, in terms of the Łojasiewicz inequality, a sufficient condition for C k -mappings germs of non-isolated singularity at zero to be isotopical.

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Cited by 5 publications
(4 citation statements)
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“…In the following theorem, the relative Kuiper-Kuo condition implies Σ-C 0 -sufficiency, is also proved, with slighly different method in [24].…”
Section: 1mentioning
confidence: 99%
See 1 more Smart Citation
“…In the following theorem, the relative Kuiper-Kuo condition implies Σ-C 0 -sufficiency, is also proved, with slighly different method in [24].…”
Section: 1mentioning
confidence: 99%
“…On the other hand, the works on characterisations of sufficiency of jets relative to a given closed set have been also started, e.g. V. Grandjean [8], S. Izumiya and S. Matsuoka [9], L. Kushner and B. Terra Leme [20], V. Thilliez [27], X. Xu [35] , P. Migus, T. Rodak and S. Spodzieja [24] and so on. This relative case includes the non-isolated case.…”
Section: Introductionmentioning
confidence: 99%
“…By a k-Z-jet in the class C k , or briefly a k-Z-jet, we mean an equivalence class w ⊂ C k 0 (n) of the following equivalence relation: f ∼ g iff for some neighbourhood U ⊂ R n of the origin, j k f (a) = j k g(a) for a ∈ Z ∩ U (cf. [27], [41]). The functions f ∈ w are called C k -Z-realizations of the jet w and we write w = j k Z f .…”
Section: Introductionmentioning
confidence: 99%
“…Obviously, there arises a natural question what happens in the case of mappings with non-isolated singularities. Rodak, Spodzieja, and the author of this paper [9] and Bekka and Koike [1] independently took that topic and obtained sufficient conditions for topological equivalence without any assumption about singularities which are straightforward generalization of the theorem of Xu.…”
mentioning
confidence: 99%