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C (X;G) be the subgroup of Ci(X;G) consisting of cochains for which there is a compact set of Xoutside of which they are zero The cohomology groups with compact supports are the cohomology groups Hi c (X;G) of this subcomplex Lemma 24 If Mis the union of two open sets Uand V, then there is a diagram of Mayer{Vietoris sequences, commutative.

C rn cxg. Write dist(x;C) = kx P C(x)k 2, where P C(x) is the projection of xonto C Then when dist(x;C) >0, @dist(x;C) = ˆ x P C(x) kx P C(x)k 2 ˙ Only has one element, so in fact dist(x;C) is di erentiable and this is its. Coquelicot i R N R j C e A X ^ C X g ΐ a @ X ^ C O { ̏Љ A R N R u O. 3 a n l ̃C x g N A( O ^ V s 莞 ̑D 𑝂₷ C x g) 123 ̃C x g N A P Z h j A ̃A X ^ Ɖ b ŃC x g.

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3 a n l ̃C x g N A( O ^ V s 莞 ̑D 𑝂₷ C x g) 123 ̃C x g N A P Z h j A ̃A X ^ Ɖ b ŃC x g. @Concrete758 ̃c C g shop info X ܏ R N g C _ X g h ƕ. Write dist(x;C) = kx P C(x)k 2, where P C(x) is the projection of xonto C It turns out that when dist(x;C) >0, @dist(x;C) = ˆ x P C(x) kx P C(x)k 2 ˙ Only has one element, so in fact dist(x;C) is di.

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