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BIFURCATION SETS OF FUNCTIONS DEFINABLE IN O-MINIMAL STRUCTURES

机译:可在O最小结构中定义的函数的分歧集

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摘要

Let g: X → Y be a C~p map between two manifolds, for some p ≥ 1, where we allow p = ∞. Let 1 ≤ q ≤ p. We say that y_0 ∈ Y is a C~q typical value of g if y_0 is a regular value of g and there exists an open neighborhood U of y_0 in Y, such that the restriction g: g~(-1)(U) → U is a C~q trivial fibration, i.e., such that there exists a C~q diffeomorphism h: g~(-1)(y_0) x U → g~(-1)(U) satisfying g(h(y, u)) = u, for all (y, u) ∈ g~(-1)(y_0) x U.
机译:令g:X→Y是两个流形之间的C〜p映射,对于某些p≥1,我们允许p =∞。令1≤q≤p。我们说如果y_0是g的正则值并且y中存在y_0的开放邻域U,则y_0∈Y是g的C〜q典型值,因此限制g:g〜(-1)(U) →U是C〜q琐碎纤维化,即存在C〜q微分形h:g〜(-1)(y_0)x U→g〜(-1)(U)满足g(h(y ,u))= u,对于所有(y,u)∈g〜(-1)(y_0)x U.

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