RT Journal Article T1 Convex sets in Banach spaces and a problem of Rolewicz A1 Granero, A. S. A1 Jiménez Sevilla, María del Mar A1 Moreno, José Pedro AB Let BX be the set of all closed, convex and bounded subsets of a Banach space X equipped with the Hausdor metric. In the rst part of this work we study the density character of BX and investigate its connections with the geometry of the space, in particular with a property shared by the spaces of Shelah and Kunen. In the second part we are concerned with the problem ofRolewicz, namely the existence of support sets, for the case of spaces C(K). PB Polish Acad Sciencies Inst Mathematics SN 0039-3223 YR 1998 FD 1998 LK https://hdl.handle.net/20.500.14352/58663 UL https://hdl.handle.net/20.500.14352/58663 LA eng NO J. M. Borwein and J. D. Vanderwer�, Banach spaces that admit support sets, Proc. Amer. Math. Soc. 124(3) 1996, 751-755.M. D�zamonja and K. Kunen, Properties of the class of measure separable compact spaces, Fund. Math. 147 (1995), 261-277.C. Finet and G. Godefroy, Biorthogonal systems and big quotient spaces, Contemporary Math. vol. 85 (1989), 87-110.J. R. Giles, D. A. Gregory, and B. Sims, Characterization of normed linear spaces with Mazur's intersection property, Bull. Austral. Math. Soc. 18 (1978), 471-476.G. Godefroy, Nicely smooth Banach spaces, The University of Texas at Austin, Functional Analysis Seminar, 1984-1985G.Godefroy, Compacts de Rosenthal, Pac. J.Math. 91(2), 1980, 293-306.B. V. Godun and S. L. Troyanski, Renorming Banach spaces with fundamental biorthogonal systems, Contemporary Math. 144 (1993), 119-126.M. Jim�enez Sevilla and J.P. Moreno, The Mazur intersection property and Asplund spaces, C.R. Acad. Sci. Paris, S�erie I, 321 (1995), 1219-1223.M. Jim�enez Sevilla and J.P. Moreno, Renorming Banach spaces with the Mazur intersection property, J. Funct. Anal. 144 (2) (1997), 486-504.M. Jim�enez Sevilla and J.P. Moreno, On denseness of certain norms in Banach spaces, Bull. Austral. Math. Soc. 54 (1996), 183-196.K. Kuratowski, Topology I, Academic Press, New York and London, 1966.D. N. Kutzarova, Convex sets containing only support points in Banach spaces with an uncountable minimal system, C. R. Acad. Bulg. Sci. 39 No. 12 (1986), 13-14.H. E. Lacey, The Isometric Theory of Classical Banach spaces, Springer-Verlag 1974.A. J. Lazar, Points of support for closed convex sets, Illinois J. Math. 25 (1981), 302{305.J. Lindenstrauss and L. Tzafriri, Classical Banach spaces II: Function spaces, Springer-Verlag, Berlin 1979.S. Mazur, � Uber schwache Konvergentz in den Raumen Lp, Studia Math. 4 (1933), 128-133.V. Montesinos, Solution to a problem of S. Rolewicz, Studia Math. 81 (1985), 65-69.S. Negrepontis, Banach spaces and Topology, Handbook of set theoretic Topology (K. Kunen and J. E. Vaughan, eds.), North-Holland, 1984, 1045-1142A. N. Plichko, A Banach space without a fundamental biorthogonal system, Soviet. Math. Dokl. 22 (1980) No. 2, 450-453.S. Rolewicz, On convex sets containing only points of support, Comment. Math., Tomus specialis in honorem Ladislai Orlicz, I, Warszawa, 1978, 279-281.W. Schachermayer, Norm attaining operators and renormings of Banach spaces, Isr. J. Math. 44 (1983), 201-212.A. Sersouri, w-independence in non-separable Banach spaces, Contemp. Math. 85 (1989), 509-512.S. Shelah, Uncountable constructions for B. A., e.c. and Banach spaces, Isr. J. Math. 51 (1985), No. 4, 273-297. NO DGICYT DS Docta Complutense RD 29 nov 2023