High Quality Content by WIKIPEDIA articles! In mathematics, topological K-theory is a branch of algebraic topology. It was founded to study vector bundles on general topological spaces, by means of ideas now recognised as (general) K-theory that were introduced by Alexander Grothendieck. The early work on topological K-theory is due to Michael Atiyah and Friedrich Hirzebruch.Let X be a compact Hausdorff space and k=mathbb{R} or k=mathbb{C}. Then Kk(X) is the Grothendieck group of the commutative monoid whose elements are the isomorphism classes of finite dimensional k-vector bundles on X with the operation.

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