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Preservation of $ \gamma$-spaces and covering properties of products


Authors: Dušan Repovš and Lyubomyr Zdomskyy
Journal: Proc. Amer. Math. Soc. 147 (2019), 4979-4985
MSC (2010): Primary 03E35, 54D20; Secondary 54C50, 03E05
DOI: https://doi.org/10.1090/proc/14593
Published electronically: July 30, 2019
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Abstract: We prove that the Hurewicz property is not preserved by finite products in the Miller model. This is a consequence of the fact that Miller forcing preserves ground model $ \gamma $-spaces.


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Additional Information

Dušan Repovš
Affiliation: Faculty of Education, and Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia
Email: dusan.repovs@guest.arnes.si

Lyubomyr Zdomskyy
Affiliation: Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Wiedner Hauptstraße 8-10/104, 1040 Wien, Austria
Email: lzdomsky@gmail.com

DOI: https://doi.org/10.1090/proc/14593
Keywords: Hurewicz space, $\gamma$-space, Miller forcing, proper forcing.
Received by editor(s): June 14, 2018
Received by editor(s) in revised form: February 12, 2019, and February 15, 2019
Published electronically: July 30, 2019
Additional Notes: The first author was partially supported by Slovenian Research Agency grants P1-0292 and N1-0083.
The second author would like to thank the Austrian Science Fund FWF (Grants I 2374-N35 and I 3709-N35) for generous support for this research.
Communicated by: Heike Mildenberger
Article copyright: © Copyright 2019 American Mathematical Society