Dichotomies pour les espaces de suites réelles
Casevitz, Pierre
Fundamenta Mathematicae, Tome 163 (2000), p. 249-284 / Harvested from The Polish Digital Mathematics Library
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There is a general conjecture, the dichotomy (C) about Borel equivalence relations E: (i) E is Borel reducible to the equivalence relation EGX where X is a Polish space, and a Polish group acting continuously on X; or (ii) a canonical relation E1 is Borel reducible to E. (C) is only proved for special cases as in [So].  In this paper we make a contribution to the study of (C): a stronger conjecture is true for hereditary subspaces of the Polish space ℝω of real sequences, i.e., subspaces such that [y=(yn)n∈X and ∀n, |xn|≤|yn|]⇒x=(xn)n∈X. If such an X is analytic as a subset of ℝω, then either X is Polishable as a vector subspace, or X admits a subspace strongly isomorphic to the space c00 of finite sequences, or to the space ℓ∞ of bounded sequences.  When X is Polishable, the metrics have a very simple form as in the case studied in [So], which allows us to study precisely the properties of those X’s

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:212469 
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     title = {Dichotomies pour les espaces de suites r\'eelles},
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     volume = {163},
     year = {2000},
     pages = {249-284},
     zbl = {0959.03032},
     language = {fra},
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Casevitz, Pierre. Dichotomies pour les espaces de suites réelles. Fundamenta Mathematicae, Tome 163 (2000) pp. 249-284. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv165i3p249bwm/

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