## Annals of Mathematics |

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abelian algebraic correspondence analytic arbitrary assume Banach space boundary bounded closed coefficients cohomology component condition consider contains continuous convergent convex Corollary coset countable curve defined definition degree denote determined differential equation dimension dimensional divisor domain element equivalent Euclidean exists extension finite number follows free group function fundamental given group G Haar measure hence homogeneous homomorphism homotopy identity implies induced infinite integral intersection invariant irreducible isomorphism Lebesgue measure Lemma Let G Lie algebra Lie group Lie subgroup linear locally compact Math measure space modulo neighborhood nilpotent nonzero norm normal normal subgroup notation obtain open set operator plane polynomial primary ring prime ideal prove real numbers relation result satisfies sequence simplicial simply connected subgroup subset subspace Suppose symbol T-set Theorem theory topological unique unitary representation values vector zero