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Topological Spaces and Groups
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abelian group Amer analytic arbitrarily small arbitrary borhood carrier circle group closed subgroup closed subset compact connected compact invariant subgroup compact neighborhood compact set compact subgroup completes the proof component connected group continuous function converges Corollary coset space countable cross-section defined definition denote differentiable dimension element of G euclidean space example exists finite number finite-dimensional fixed follows given group G Hausdorff space Hence homeomorphism homogeneous space identity inner point integer inverse Lemma Let G Lie group linear locally compact group locally euclidean manifold Math matrix metric space natural map neigh one-one one-parameter group one-parameter local group open set open subgroup orbit orthogonal group properties proved real number sequence shows small subgroups subgroup H subgroup of G Suppose symmetric neighborhood theorem three-space topological group topological space totally disconnected transformation group union unique vector zero