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A Stone-Weierstrass theorem for certain discontinuous functions

  • Bruno Brosowski
  • Antonio R. da Silva
Article

Abstract

Let A be point separating unital subalgebra of C(T) where T is a compact metric space. For each bounded function f:T→R which is continuous on the complement of a meagre subset of T there exists a sequence (wn) of elements of the algebra A such that the sequence (wn) convergence uniformly to the function f on each compact subset of the interior of the continuity points of the function f.

Keywords

Compact Subset Hausdorff Space Discontinuous Function Compact Hausdorff Space Continuity Point 
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.

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References

  1. [1]
    Bierstedt, K. D., Verallgemeinerungen des Satzes von Stone-Weierstrass, in: Jahrbuch Überblicke Mathematik (1975), 109–135.Google Scholar
  2. [2]
    Prolla, J.B., Weierstrass-Stone, the Theorem, Peter Lang Verlag, Frankfurt, 1993.MATHGoogle Scholar

Copyright information

© Springer 1997

Authors and Affiliations

  • Bruno Brosowski
    • 1
  • Antonio R. da Silva
    • 2
  1. 1.Fachbereich MathematikJohann Wolfgang Goethe-UniversitätFrankfurt a.M.F. R. Germany
  2. 2.Instituto de MatemáticaUniversidade Federal do Rio de JaneiroRio de Janeiro CEPBrazil

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