Normed versus topological groups: Dichotomy and duality

Normed groups 143Series 378, 2010.[BOst-StOstr] N. H. Bingham and A. J. Ostaszewski, Dichotomy and Infinite Combinatorics:the theorems of Steinhaus and Ostrowski, Math. Proc. Camb.Phil. Soc., in press.[Bir] G. Birkhoff, A note on topological groups, Compositio Math. 3 (1936),427–430.[BlHe] W. Bloom and H. Heyer, Harmonic analysis of probability measures onhypergroups, de Gruyter Studies in Mathematics, 20. Walter de Gruyter& Co., Berlin, 1995.[Bo] T. Bökamp, Extending norms on groups, Note Mat. 14.2 (1994), 217-227.[Bor] K. C. Border, Fixed point theorems with applications to economics andgame theory, Cambridge University Press, 1989.[BoDi] D. Borwein and S. Z. Ditor, Translates of sequences in sets of positivemeasure, Canadian Mathematical Bulletin 21 (1978), 497-498.[Bour] N. Bourbaki, Elements of mathematics: General topology. Parts 1 and2. Hermann, Paris; Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont. 1966.[Bou1] A. Bouziad, The Ellis theorem and continuity in groups, Topology Appl.50 (1993), no. 1, 73–80.[Bou2] A. Bouziad, Every Čech-analytic Baire semitopological group is a topologicalgroup, Proc. Amer. Math. Spc. 124.3 (1996), 953-959.[BH]M. R. Bridson and A. Haefliger, Metric spaces on non-positive curvature,Springer 1999.[Br-1] L. G. Brown, Note on the open mapping theorem. Pacific J. Math. 38(1971), 25–28.[Br-2] L. G. Brown, Topologically complete groups, Proc. Amer. Math. Soc. 35(1972), 593–600.[CSC] F. Cabello Sánchez, and J. M.F Castillo, Banach space techniques underpinninga theory for nearly additive mappings. Dissertationes Math.(Rozprawy Mat.) 404 (2002), 73pp.[CaMo] J. Cao, and W.B Moors, Separate and joint continuity of homomorphismsdefined on topological groups. New Zealand J. Math. 33 (2004), no. 1,41–45.[ChMa] J. J. Charatonik and T. Maćkowiak, Around Effros’ theorem, Trans.Amer. Math. Soc. 298.2 (1986), 579–602.[Choq] G. Choquet, Theory of capacities, Ann. Inst. Fourier, Grenoble 5 (1953-54), 131-295.[Ch]J. P. R. Christensen, Topology and Borel structure. Descriptive topologyand set theory with applications to functional analysis and measuretheory. North-Holland Publishing Co., Amsterdam-London; AmericanElsevier Publishing Co., Inc., New York, 1974.[Com] W. W. Comfort, Topological groups, Ch. 24 in [KuVa].[Csa] A. Császár, Konvex halmazokról és fuggvényegyenletekröl (Sur les en-