Paratingent cone
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 called a tangent (or tangent vector) to  at , if there is a sequence  of elements  and a sequence  of positive real numbers  such that  and 
 The set  of all tangents 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

References

Mathematical analysis