On the complexity of subspaces of $S_{ω}$

Carlos Uzcátegui

On the complexity of subspaces of

S_{ω}

Carlos Uzcátegui

Fundamenta Mathematicae, Tome 177 (2003), p. 1-16 / Harvested from The Polish Digital Mathematics Library

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Résumé

Let (X,τ) be a countable topological space. We say that τ is an analytic (resp. Borel) topology if τ as a subset of the Cantor set $2^{X}$ (via characteristic functions) is an analytic (resp. Borel) set. For example, the topology of the Arkhangel’skiĭ-Franklin space $S_{ω}$ is $F_{σ δ}$ . In this paper we study the complexity, in the sense of the Borel hierarchy, of subspaces of $S_{ω}$ . We show that $S_{ω}$ has subspaces with topologies of arbitrarily high Borel rank and it also has subspaces with a non-Borel topology. Moreover, a closed subset of $S_{ω}$ has this property iff it contains a copy of $S_{ω}$ .

Publié le : 2003-01-01

Zbl 1027.54055

EUDML-ID : urn:eudml:doc:282681

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     title = {On the complexity of subspaces of $S\_{$\omega$}$
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Carlos Uzcátegui. On the complexity of subspaces of $S_{ω}$
            . Fundamenta Mathematicae, Tome 177 (2003) pp. 1-16. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm176-1-1/