Properties of countable separation and implicit function theorem

  • Cristina M. Di Bari
  • Pasquale Vetro


We consider some properties of countable separation for familiesA andD of subsets of a setX by means of elements of a fixed familyMP(X). We give necessary and sufficient conditions, in terms of measurability of some sets constructed by means of multifunctions, in order that the familiesA andD satisfy such a property. As an application we derive an implicit function theorem for functions ofCarathéodory-type.


Topological Space Measurable Space Closed Subset Implicit Function Theorem Countable Family 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Averna D.,Separation properties in X and 2X.Upper semicontinuous and measurable multifunctions, Rend. Circ. Mat. Palermo38 (1989), 140–151.MATHMathSciNetCrossRefGoogle Scholar
  2. [2]
    Averna D.,Separation properties in X and 2X:measurable multifunctions and graphs, Mat. Cas. (to appear).Google Scholar
  3. [3]
    Cristensen J. P. R.,Topology and Borel structure, North-Holland Amsterdam, 1974.Google Scholar
  4. [4]
    Di Bari C. M.,Measurability and countable separation, Rend. Circ. Mat. Palermo39 (1990).Google Scholar
  5. [5]
    Dravecký J.Spaces with measurable diagonal, Mat. Čas.25 (1975), 3–9.MATHGoogle Scholar
  6. [6]
    Dravecký J.—Neubrunn T.Measurability of functions of two variables Mat. Čas.23 (1973), 147–157.MATHGoogle Scholar
  7. [7]
    Hou S. H.,Implicit function theorem in topological space, Appl. Analysis13 (1982), 209–217.MATHCrossRefGoogle Scholar
  8. [8]
    Sainte-Beuve M.-F.,On the extension of von Neumann-Aumann’s theorem, J. Functional Analysis17 (1974), 112–129.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer 1990

Authors and Affiliations

  • Cristina M. Di Bari
    • 1
  • Pasquale Vetro
    • 1
  1. 1.Dipartimento di Matematica ed ApplicazioniPalermo

Personalised recommendations