In mathematics, Kuiper's theorem (after Nicolaas Kuiper) is a result on the topology of operators on an infinite-dimensional, complex Hilbert space H. It states that the space GL(H) of invertible bounded endomorphisms H is such that all maps from any finite complex Y to GL(H) 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.
Read more about Kuiper's Theorem: General Topology of The General Linear Group, Historical Context and Topology of Spheres, Bott's Unitary Group, Applications, Case of Banach Spaces
Famous quotes containing the word theorem:
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)