Topological Groups

abstract group automorphism axiom of countability belong canonical coordinates character group closed set coincides commutative group compact group compact topological group complete system construction contains continuous function converges corresponds cosets curve decomposes defined on G denote by G differentiable or analytic direct product direct sum elements of G equations exists a neighborhood factor group finite number finite system function f(x G and G groups isomorphic H₁ Hence homomorphic mapping identity infinitesimal group integral intersection isomorphic mapping Let G Let us denote limit point linear linearly independent local Lie group locally compact locally isomorphic mapping g matrix one-parameter subgroup open set orthogonal path positive number proof proposition prove readily be seen real numbers relation satisfying the second second axiom sequence set G space G structural constants subgroup H subset system of neighborhoods Theorem 32 tion topological group satisfying topological space transformation U₁ uniquely whole group