Let G be a compact definable C r group and 1 ≤ r < ∞.We prove that if X is a noncompact affine definable C r G manifold and X 1 , . . ., X n are noncompact definable C r G submanifolds of X in general position such that (X; X 1 , . . ., X n ) satisfies the frontier condition, then (X;Furthermore we prove that we can raise simultaneously differentiability of a definable C 2 manifold and its definable C 2 submanifolds such that they satisfy some condition.
Tomohiro KAWAKAMI (Sat,) studied this question.
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