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{{Short description|Exact homotopy case}}
{{DISPLAYTITLE:Classifying space for U(''n'')}}
In [[mathematics]], the '''[[classifying space]] for the [[unitary group]]''' U(''n'') is a space BU(''n'') together with a universal bundle EU(''n'') such that any hermitian bundle on a [[paracompact space]] ''X'' is the pull-back of EU(''n'') by a map ''X'' → BU(''n'') unique up to homotopy.
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