RT Journal Article T1 A characterization of K-analyticity of groups of continuous homomorphisms A1 Kąkol, Jerzy A1 Martín Peinador, Elena A1 Moll, Santiago AB For an abelian locally compact group X let X^p be the group of continuous homomorphisms from X into the unit circle T of the complex plane endowed with the pointwise convergence topology. It is proved that X is metrizable iff X^p is K-analytic iff X endowed with its Bohr topology σ(X,X^) has countable tightness. Using this result, we establish a large class of topological groups with countable tightness which are not sequential, so neither Fréchet-Urysohn PB Sociedad Matemática Mexicana SN 1405-213X YR 2008 FD 2008 LK https://hdl.handle.net/20.500.14352/50675 UL https://hdl.handle.net/20.500.14352/50675 LA eng NO L. Aussenhofer, Contributions to the duality of abelian topological groups and to the theory of nuclear groups, Dissert. Math. 384. Warszawa 1999.A. V. Arkhangel'skii, Topological function spaces, Math. and its Appl. Kluwer (1992).W. Banaszczyk, Additive Subgroups of Topological Vector Spaces, Springer Verlag LNM, 1446 (1991).J. Calbrix, Espaces Kσ et espaces des applicacions continues, Bull. Soc. Math. France 113, (1985), 183-203.M. J. Chasco, Pontryagin duality for metrizable groups, Arch. Math. 70, (1998), 22-28.M. J. Chasco, E. Martín-Peinador, V. Tarieladze, A class of angelic sequential non-Fréchet-Urysohn topological groups, Topol. Appl. 154, (2007), 741-748.J. P. R. Christensen, Topology and Borel structure, North-Holland Math. Studies 10, (1974).J. Cleary, S. A. Morris, Topologies on locally compact groups, Bull. Australian Math. Soc. 38 (1988), 105-111.H. H. Corson, The weak topology of a Banach space, Trans. Amer. Math.Soc. 101 (1961), 1-15.E. Hewitt, K. A. Ross, Abstract Harmonic Analysis I, Springer, Berlin, New York, 1979.K. H. Hofmann, S. A. Morris, The structure of compact groups, Studies in Math. 25, (1998).J. Kąkol, M. López Pellicer, E. Martín-Peinador and V. Tarieladze, Lindelöf spaces C(X) over topological groups, Forum Math. 20 (2008), 201-212.R. A. McCoy, I. Ntantu, Topological Properties of Spaces of Continuous Functions, Lecture Notes in Math. 1988.S. A. Morris, Pontryagin duality and the structure of locally compact abelian groups, London Math. Soc. Lecture Note Series 29, (1977).E. Martín-Peinador, V. Tarieladze, Aproperty of Dunford-Pettis type in topological groups, Proc. Amer. Math. Soc. 132 (2004), 1827-1834.M. Talagrand, Espaces de Banach faiblement K-analytiques, Ann. Math. 119 (1979), 407-438 NO Spanish Ministery of Education and Science NO European Community (Feder projects) NO Ministry of Science and Higher Education, Poland NO Proyectos de Investigación Santander-Complutense NO Primeros Proyectos de Investigacióon UPV PAID-06-06 DS Docta Complutense RD 30 abr 2024