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A Stone-Weierstrass theorem for certain discontinuous functions |
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| Authors: | Bruno Brosowski Antonio R. da Silva |
| Affiliation: | 1. Fachbereich Mathematik, Johann Wolfgang Goethe-Universit?t, Robert Mayer-Str. 6-10, D-60054, Frankfurt a.M., F. R. Germany 2. Instituto de Matemática, Universidade Federal do Rio de Janeiro, 21945-970, Rio de Janeiro CEP, Brazil |
| 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. |
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