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Non-meager free sets for meager relations on Polish spaces


Authors: Taras Banakh and Lyubomyr Zdomskyy
Journal: Proc. Amer. Math. Soc. 143 (2015), 2719-2724
MSC (2010): Primary 54E52, 54E50; Secondary 54D80
DOI: https://doi.org/10.1090/S0002-9939-2015-12419-7
Published electronically: February 16, 2015
MathSciNet review: 3326049
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Abstract: We prove that for each meager relation $ E\subset X\times X$ on a Polish space $ X$ there is a nowhere meager subspace $ F\subset X$ which is $ E$-free in the sense that $ (x,y)\notin E$ for any distinct points $ x,y\in F$.


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Additional Information

Taras Banakh
Affiliation: Department of Mathematics, Ivan Franko National University of Lviv, Ukraine – and – Instytut Matematyki, Jan Kochanowski University, Kielce, Poland
Email: t.o.banakh@gmail.com

Lyubomyr Zdomskyy
Affiliation: Kurt Gödel Research Center for Mathematical Logic, University of Vienna, Währinger Straße 25, A-1090 Wien, Austria
Email: lzdomsky@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-2015-12419-7
Keywords: Meager relation, free set
Received by editor(s): April 9, 2013
Received by editor(s) in revised form: October 28, 2013
Published electronically: February 16, 2015
Additional Notes: The first author was partially supported by NCN grants DEC-2011/01/B/ST1/01439 and DEC-2012/07/D/ST1/02087
The second author was a recipient of an APART-fellowship of the Austrian Academy of Sciences
Communicated by: Mirna Dzamonja
Article copyright: © Copyright 2015 American Mathematical Society

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