On the Euler characteristic of the links of a set determined by smooth definable functions
نویسنده
چکیده
Consider a polynomially bounded, o-minimal structure on the field R of reals. A smooth (i.e. of class C∞) definable function φ : U −→ R on an open set U in R determines two closed subsets W := {u ∈ U : φ(u) ≤ 0} and Z := {u ∈ U : φ(u) = 0}. We shall investigate the links of the sets W and Z at the points u ∈ U , which are well-defined up to a definable homeomorphism. It is proven that the Euler characteristic of those links (being a local topological invariant) can be expressed as a finite sum of signs of global smooth definable functions:
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تاریخ انتشار 2006