On open maps of Borel sets

Tom 146 / 1995

A. Ostrovsky Fundamenta Mathematicae 146 (1995), 203-213 DOI: 10.4064/fm-146-3-203-213

Streszczenie

We answer in the affirmative [Th. 3 or Corollary 1] the question of L. V. Keldysh [5, p. 648]: can every Borel set X lying in the space of irrational numbers ℙ not $G_δ · F_σ$ and of the second category in itself be mapped onto an arbitrary analytic set Y ⊂ ℙ of the second category in itself by an open map? Note that under a space of the second category in itself Keldysh understood a Baire space. The answer to the question as stated is negative if X is Baire but Y is not Baire.

Autorzy

  • A. Ostrovsky

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