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Banach Space Theory and its Applications pp 103–110Cite as

On Etcheberry’s extended Milutin lemma

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 991))

Abstract

If X is an uncountable Polish space, then the space BC(X) of bounded continuous functions on X is a factor of BC(I), where I denotes the set of irrational numbers. Etcheberry proved this by constructing a continuous surjection π: I→X that admits an averaging operator. Here, we provide an alternative technique for the construction of averaging operators that are even regular and also allow one to prove the first mentioned result.

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References

  1. R.D. ANDERSON and R.H. BING, A completely elementary proof that Hilbert space is homeomorphic to the countable product of lines, Bull. Amer. Math. Soc. 74 (1968), 771–792

    Article  MathSciNet  MATH  Google Scholar 

  2. L. BLUMENTHAL and V. KLEE, On metric independence and linear independence, Proc. Amer. Math. Soc. 6 (1955), 732–734

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  3. A. ETCHEBERRY, Isomorphisms of spaces of bounded continuous functions, Studia Math. 53 (1979), 103–127

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  4. V. KLEE, On the Borelian and Projective Types of Linear Subspaces, Math. Scand. 6 (1958), 189–199

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  5. K. KURATOWSKI, Sur une généralisation de la notion d'homéomorphie Fundam. Math. 22 (1934), 206–220

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  6. E. MICHAEL, Some extension theorems for continuous functions, Pacific J. Math. 3 (1953), 789–806

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  7. Z. SEMADENI, Banach spaces of continuous functions, Warszawa, 1971

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Author information

Authors and Affiliations

  1. Dept. of Mathematics, University of Regensburg, 84 Regensburg, Germany

    H. U. Hess

Authors
  1. H. U. Hess
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Albrecht Pietsch Nicolae Popa Ivan Singer

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© 1983 Springer-Verlag

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Hess, H.U. (1983). On Etcheberry’s extended Milutin lemma. In: Pietsch, A., Popa, N., Singer, I. (eds) Banach Space Theory and its Applications. Lecture Notes in Mathematics, vol 991. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0061562

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  • DOI: https://doi.org/10.1007/BFb0061562

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12298-2

  • Online ISBN: 978-3-540-39877-6

  • eBook Packages: Springer Book Archive

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