Normed versus topological groups: Dichotomy and duality

Normed groups 145abelian groups, Math. Scand. 2 (1954), 5-18.[For] M. K. Fort Jr., A unified theory of semi-continuity, Duke Math. J. 16(1949), 237–246.[Fos]M. Fosgerau, When are Borel functions Baire functions? Fund. Math.143 (1993), no. 2, 137–152.[FrKu] R. Frankiewicz, K. Kunen, Solution of Kuratowski’s problem on functionhaving the Baire property. I, Fund. Math. 128.3 (1987), 171–180.[Frem] D. H. Fremlin, Measure-additive coverings and measurable selectors, DissertationesMath. (Rozprawy Mat.) 260 (1987), 116pp.[Fre-4] D. H. Fremlin, Measure theory. Vol. 4. Topological measure spaces. PartI, II. Corrected second printing of the 2003 original. Torres Fremlin,Colchester, 2006.[Frol-60] Z. Frolík, Generalizations of the G δ -property of complete metric spaces,Czechoslovak Math. J 10 (85) 1960 359–379.[Fu]L. Fuchs, Infinite abelian groups, Vol. I. Pure and Applied MathematicsVol. 36, Academic Press, 1970.[Ful]R.V. Fuller, Relations among continuous and various non-continuousfunctions, Pacific J. Math. 25 1968 495–509.[Ga]J. Gallian, Contemporary Abstract Algebra, 4th edition, Houghton Mifflin,Boston, 1998.[GJ]L. Gillman and M. Jerison, Rings of continuous functions. Van Nostrand,1960 (reprinted as Graduate Texts in Mathematics 43, Springer-Verlag,1976).[GNN] C. Goffman, C. J. Neugebauer and T. Nishiura, Density topology andapproximate continuity, Duke Math. J. 28 (1961), 497–505.[GoWa] C. Goffman, D. Waterman, Approximately continuous transformations,Proc. Amer. Math. Soc. 12 (1961), 116–121.[GRS] R. L. Graham, B. L. Rothschild, J. H. Spencer, Ramsey theory, Secondedition. Wiley, 1990 (1st. ed. 1980).[Gr1] M. Gromov, Hyperbolic manifolds, groups and actions. Riemann surfacesand related topics, Proceedings of the 1978 Stony Brook Conference(State Univ. New York, Stony Brook, N.Y., 1978), pp. 183–213. Ann. ofMath. Stud., 97, Princeton Univ. Press, Princeton, N.J., 1981.[Gr2] M. Gromov, Groups of polynomial growth and expanding maps. Inst.Hautes Études Sci. Publ. Math. No. 53 (1981), 53–73.[Hal-M] P. R. Halmos, Measure Theory, D. Van Nostrand, 1950 (Graduate Textsin Math. 18, Springer, 1979).[Hal-ET] P. R. Halmos, Lectures on ergodic theory, Chelsea Publ. Co., New York,1956.[HT]G. Hansel and J-P. Troallic, Quasicontinuity and Namioka’s theorem,Topology Appl. 46 (1992), no. 2, 135–149.[Han-71] R. W. Hansell, Borel measurable mappings for nonseparable metricspaces, Trans. Amer. Math. Soc. 161 1971 145–169.