A Stone-Weierstrass theorem for certain discontinuous functions

  • Bruno Brosowski
  • Antonio R. da Silva


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.


Compact Subset Hausdorff Space Discontinuous Function Compact Hausdorff Space Continuity Point 


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  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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