Locally Compact Semigroups in which a Subgroup with Compact Complement is Dense: Homogeneous Locally Compact Groups with Compact Boundary1966 - Topology - 172 pages |
Common terms and phrases
A(Ce abelian group additive group additive reals algebraic C₁ central subgroup circle group closure clusterpoint compact boundary compact connected group compact neighborhood compact normal subgroups compact open subgroup compact set compact space compact topological group congruence relation connected compact connected subspace continuous mapping converging countable cyclic group defined dense subgroup direct product division rings finishes the proof finite dimensional G contains group with compact group with zero Hausdorff Hence identity implies inner automorphism intersection kernel left cosets modulo Lemma Let G Lie group lim g limit of Lie locally compact group locally compact topological maximal compact open maximal compact subgroup maximal subgroup multiplicative semigroup non-negative reals normal in G one-parameter group one-parameter subgroup open neighborhood point compactification positive reals projective limit Proposition prove quotient space real numbers reals under multiplication S₁ S₂ sequence subgroup G subgroup of G subsemigroup subset theorem topological semigroup totally disconnected trivial