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What is a transversality?

What is a transversality? Here are some definitions.

Noun
  1. (mathematics) a property of two intersecting submanifolds, where at every intersection point, their separate tangent spaces at that point together generate the tangent space of the ambient manifold at that point.
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Examples
In my opinion, this constitutes a twofold error, because, even if the concept of transversality is a good one, in practice it is completely unrealistic.
We actively encourage transversality and exchanges so as to constitute a genuine strength.
The method is an application of the weak transversality theorem used in catastrophe theory.
The request for transversality of fundamental and human rights must also, and especially, be taken into account in the Union's foreign policy.
Taking account of tourism's transversality calls for both a sound knowledge of the diversity of subjects involved and real professionalism, and thus for the development of new and complementary skills.
Given a closed Riemannian manifold M, we construct a suitable class of perturbations to achieve Morse-Smale transversality for the heat equation.

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