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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© 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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