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[[Category:Topology]][[Category:Theorems]]▼
In [[mathematics]], the '''Brouwer fixed point theorem''' states that every [[continuous]] [[function (mathematics)|function]] from the closed unit ball ''D''<sup> ''n''</sup> to itself has a [[fixed point (mathematics)|fixed point]]. In this theorem, ''n'' is any positive [[integer]], and the closed unit ball is the set of all points in [[Euclidean space|Euclidean ''n''-space]] '''R'''<sup>''n''</sup> which are at distance at most 1 from the origin.
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*For a number of generalizations of the Brouwer fixed point theorem to infinite dimensions, see [[fixed point theorems in infinite-dimensional spaces]].
▲[[Category:Topology]][[Category:Theorems]]
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