Brouwer fixed-point theorem: Difference between revisions

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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''^&nbsp;''n'' 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 <i>n</i>-space]] '''R'''^''n'' which are at distance at most 1 from the origin.