On open maps of Borel sets

A. Ostrovsky

ArticleOriginal scientific text

Title

On open maps of Borel sets

Authors ¹

Affiliations

Marine Technical University, Lotzmanskaya Str. 3, St. Petersburg, 190006, Russia

Abstract

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} \cdot 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.

Keywords

ENG

open maps, Borel sets, analytic sets, space of the first category, space of the second category, Baire space

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Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm146/fm14631.pdf

Title

On open maps of Borel sets

Affiliations

Abstract

Keywords

Bibliography

Additional information