In mathematics, a coercive function is a function that "grows rapidly" at the extremes of the space on which it is defined. More precisely, a function f : Rn → Rn is called coercive if
where "" denotes the usual dot product and denotes the usual Euclidean norm of the vector x.
More generally, a function f : X → Y between two topological spaces X and Y is called coercive if for every compact subset J of Y there exists a compact subset K of X such that
The composition of a bijective proper map followed by a coercive map is coercive.
Read more about Coercive Function: Coercive Operators and Forms
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