1 Introduction ................................................. 5
2 Metric versus normed groups .................................. 7
3 Normed versus topological groups ............................ 28
3.1 Left-versus right-shifts: Equivalence Theorem .......... 28
3.2 Lipschitz-normed groups ................................ 41
3.3 Cauchy dichotomy ....................................... 48
4 Subadditivity ............................................... 64
5 Generic dichotomy ........................................... 68
6 Steinhaus theory and dichotomy .............................. 76
7 The Kestelman-Borwein-Ditor Theorem: a bi-topological
approach .................................................... 85
8 The Subgroup Theorem ........................................ 94
9 The Semigroup Theorem ....................................... 95
10 Convexity ................................................... 98
11 Automatic continuity: the Jones-Kominek Theorem ............ 105
12 Duality in normed groups ................................... 117
13 Divergence in the bounded subgroup ......................... 123
References .................................................... 127
Index ......................................................... 136
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