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In mathematics, Kuiper's theorem is a result on the topology of operators on an infinite-dimensional, complex Hilbert space H. It states that the space GL of invertible bounded endomorphisms of H is such that all maps from any finite complex Y to GL are homotopic to a constant, for the norm topology on operators.
A significant corollary, also referred to as Kuiper's theorem, is that this group is weakly contractible, ie. all its homotopy groups are trivial. This result has important uses in topological K-theory.
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