Coercive function

In mathematics coercive function is a function $f:X\to Y$ between topological spaces X and Y such that for every compact set $J\subset Y$ there exists a compact set $K\subset X$ such that $f(X\setminus K)\subset Y\setminus J.$

The general definition given above is made clear when specialized to the Euclidean spaces: A function $f:\mathbb {R} ^{n}\to \mathbb {R} ^{m}$ is coercive if and only if $\lim _{\|x\|\to +\infty }\|f(x)\|=+\infty .$