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Bulletin of the Faculty of Education, Wakayama University. Natural science 58
2008-02-29 発行
Definable C^r groups and proper definable actions
デファイナブルC^r群と固有デファイナブル作用
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Language
eng
Start Page
9
End Page
18
Keywords Alternative
Definable groups
definable C^r groups
o-minimal
definable C^r fiber bundles
definable G sets
definable slices
proper
definable G imbeddings
Abstract Alternative
Let M=(R,+,・,<,...) be an o-minimal expansion of the standard structure R=(R,+,・,<) of the field of real numbers. Let G be a definable C^r group and H a definable C^r subgroup of G. We prove that if M. admits the C^ω (resp. C^∞) cell decomposition or 0 ≤ r < ∞, then the orbit map π : G → G
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