Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 6
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Todorcevic, Stevo 1997. Topics in Topology.

    Čoban, M. M. Kenderov, P. S. and Revalski, J. P. 1995. Topological spaces related to the Banach-Mazur game and the generic well-posedness of optimization problems. Set-Valued Analysis, Vol. 3, Issue. 3, p. 263.

    Debs, Gabriel and Raymond, Jean Saint 1994. Topological games and optimization problems. Mathematika, Vol. 41, Issue. 01, p. 117.

    Stegall, Charles 1991. The topology of certain spaces of measures. Topology and its Applications, Vol. 41, Issue. 1-2, p. 73.

    Čoban, M. M. Kenderov, P. S. and Revalski, J. P. 1989. Generic well-posedness of optimization problems in topological spaces. Mathematika, Vol. 36, Issue. 02, p. 301.

    Ribarska, N. K. 1987. Internal characterization of fragmentable spaces. Mathematika, Vol. 34, Issue. 02, p. 243.


Topological spaces with dense subspaces that are homeomorphic to complete metric spaces and the classification of C(K) Banach spaces

  • Charles Stegall (a1)
  • DOI:
  • Published online: 01 February 2010

In [S1] we introduced and in [S2, S3, S4] developed a class of topological spaces that is useful in the study of the classification of Banach spaces and Gateaux differentiation of functions defined in Banach spaces. The class C may be most succinctly defined in the following way: a Hausdorff space T is in C if any upper semicontinuous compact valued map (usco) that is minimal and defined on a Baire space B with values in T must be point valued on a dense Gδ subset of B. This definition conceals many interesting properties of the family C. See [S2] for a discussion of the various definitions. Our main result here is that if X is a Banach space such that the dual space X* in the weak* topology is in C and K is any weak* compact subset of X* then the extreme points of K contain a dense, necessarily Gδ, subset homeomorphic to a complete metric space. In [S4] we studied the class K of κ-analytic spaces in C. Here we shall show that many elements of K contain dense subsets homeomorphic to complete metric spaces. It is easy to see that C contains all metric spaces and it is proved in [S4] that analytic spaces are in K. We obtain a number of topological results that may be of independent interest. We close with a discussion of various examples that show the interaction of these ideas between functional analysis and topology

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

Ja.R. C. James . A separable somewhat reflexive Banach space with nonseparable dual. Bull Amer. Math. Soc., 80 (1974), 738743.

Ne.S. Negrepontis . Banach Spaces and Topology, in Handbook of Set Theoretic Topology (North Holland, Amsterdam, 1984).

Ro.H. Rosenthal . Pointwise compact sets of the first Baire class. Amer. Jour. Math., 99 (1977), 362378.

S5.C. Stegall . The Radon-Nikodym property in conjugate Banach spaces. Trans. Amer. Math. Soc., 206 (1975), 213223.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

  • ISSN: 0025-5793
  • EISSN: 2041-7942
  • URL: /core/journals/mathematika
Please enter your name
Please enter a valid email address
Who would you like to send this to? *