In mathematics, the paratingent cone and contingent cone were introduced by , and are closely related to tangent cones.
Definition Let be a nonempty subset of a real normed vector space .
Let some be a point in the closure of . An element is tangent to at if there is a sequence of elements and a sequence of positive real numbers such that and The set of all that are tangent to at is called the contingent cone (or the Bouligand tangent cone) to at .
An equivalent definition is given in terms of a distance function and the limit infimum. As before, let be a normed vector space and take some nonempty set . For each , let the distance function to be
Then, the contingent cone to at is defined by
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