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Algebraic and topological K-theory, relations with topology, commutative algebra, and operator algebras

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Finite dimensional real division algebras

If you ask for a purely algebraic proof, algebraic K-theory is (almost) OK. Indeed for a compact Hausdorff space $X$, it's topological K-theory $K(X)$ is the same as algebraic K-theory $K_0(C(X;\math …
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