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# coercive function

###### Definition 1 (coercive function).

Let $X$ and $Y$ be topological spaces.
A function $f\colon X\to Y$ is said to be *coercive* if 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 has a clear sense when specialized to the Euclidean spaces, as shown in the following result.

###### Proposition 1 (coercive functions on $\mathbb{R}^{n}$).

A function $f\colon\mathbb{R}^{n}\to\mathbb{R}^{m}$ is coercive if and only if

$\lim_{{|x|\to+\infty}}|f(x)|=+\infty.$ |

Synonym:

coercive, coercitive, coercitive function

Type of Math Object:

Definition

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Reference

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new question: Prove a formula is part of the Gentzen System by LadyAnne

Mar 30

new question: A problem about Euler's totient function by mbhatia

new problem: Problem: Show that phi(a^n-1), (where phi is the Euler totient function), is divisible by n for any natural number n and any natural number a >1. by mbhatia

new problem: MSC browser just displays "No articles found. Up to ." by jaimeglz

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new correction: Misspelled name by DavidSteinsaltz

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new correction: underline-typo by Filipe

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new correction: cocycle pro cocyle by pahio

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new image: plot W(t) = P(waiting time <= t) (2nd attempt) by robert_dodier

new image: expected waiting time by robert_dodier

new image: plot W(t) = P(waiting time <= t) by robert_dodier