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The Standard Borel Space of All Separable Banach Spaces

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1993)

Abstract

In this chapter we will present the general framework on which the main results contained in these notes are based. This framework has been defined by Bossard in his Thesis [Bos1]. The central idea is that, while the collection of all separable Banach spaces is not a set, it can be naturally “coded” as a standard Borel space. This coding has been proved to be compatible with any notion, construction or operation encountered in Banach Space Theory. By now it has found sufficiently many applications in order to be considered as one of its internal parts.

Keywords

  • Banach Space
  • Basic Sequence
  • Borel Subset
  • Separable Banach Space
  • Convex Banach Space

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Correspondence to Pandelis Dodos .

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© 2010 Springer-Verlag Berlin Heidelberg

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Dodos, P. (2010). The Standard Borel Space of All Separable Banach Spaces. In: Banach Spaces and Descriptive Set Theory: Selected Topics. Lecture Notes in Mathematics(), vol 1993. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12153-1_2

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