Normed versus topological groups: Dichotomy and duality

Indexabelian, 4Abelian Normability of H(X), 39admissibilityCauchy (C-adm), 51metric, 18norm, 18, 37topological , 18admissibilityweak (W-adm), 51almost complete, 72ambidextrous refinement, 32ambidextrous uniformity, 10, 54amenable, 5analytic, 112Analytic Automaticity Th., 125Analytic Dichotomy Lemma – Spanning, 119asymptotically multiplicative, 21Auth(X), 6Averaging Lemma, 104Baire, 49Baire Continuity Th., 115Baire function, 114Baire Homomorphism Th., 117Baire-continuous, 114Baire-measurable, 114Banach-Kuratowski Th., 88Banach-Mehdi Th., 116Banach-Neeb Theorem, 115Bartle’s Inverse Function Th., 111Bernstein-Doetsch Th., 107bi-Cauchy, 49Bi-Cauchy completion, 54bi-invariant (not) – SL(2, R), 38Bi-Lipschitz property, 43bi-uniformly continuous, 33, 126Borel/analytic inversion, 56bounded, 20bounded elements, 15[138]C-sets, 114Cauchy dichotomy, 49centre, 44Z γ (G), norm centre, 44CET-Category Embedding Th., 81Choquet’s Capacitability Theorem, 120class C ′ , 110closed graph, 46Combinatorial Uniform Boundedness Th.,95Common Basis Th., 101commutator, 23Compact Contraction Lemma, 120Compact Spanning Approximation, 121compact-open topology, 17completely metrizable, 71conjugacy refinement norm, 17Conjunction Th., 102converges to the identity, 133, 135convex, 104Crimping Th., 35d X R , 5Darboux norm, 123Darboux’s Th., 49Darboux-normed , 55Dense Oscillation Th., 62Density Topology Th., 91density-preserving, 79derivative, 110Dichotomy Th., convex functions, 108Displacements Lemma – Baire, 75Displacements Lemma – measure, 76diverges uniformly, 133divisible – 2-divisible, 103divisible – infinitely divisible, 14ε-shifting point, 61Effros’ Open Mapping Principle, 35