Let us consider in ℝ2 two smoothly embedded circles C 1, C 2 (i.e. C 1 and C 2 are manifolds in ℝ2 which are diffeomorphic to the circle S 1, cf. Fig. 7.1.1.a). C 1 and C 2 are called transversal at an intersection point \(\bar x\) if at this point they intersect under an angle unequal to 0 or π; more formally, this means: the tangent spaces of C 1, C 2 at \(\bar x\) span the whole ℝ2 (= space of embedding), cf. Fig. 7.1.1.b. In case of nontransversal intersection, the tangent spaces of C l and C 2 at the intersection point coincide, thus spanning a one-dimensional subspace of ℝ2 (Fig. 7.1.1.c).
KeywordsTangent Space Dense Part Open Part Generic Subset Transversal Intersection
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