Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Request Permissions   Purchase Content 
 

 

Additivity of the Gerlits-Nagy property and concentrated sets


Authors: Boaz Tsaban and Lyubomyr Zdomskyy
Journal: Proc. Amer. Math. Soc. 142 (2014), 2881-2890
MSC (2010): Primary 03E17, 26A03, 03E75
DOI: https://doi.org/10.1090/S0002-9939-2014-12012-0
Published electronically: May 2, 2014
MathSciNet review: 3209341
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We settle all problems concerning the additivity of the Gerlits-Nagy property and related additivity numbers posed by Scheepers in his tribute paper to Gerlits. We apply these results to compute the minimal number of concentrated sets of reals (in the sense of Besicovitch) whose union, when multiplied with a Gerlits-Nagy space, need not have Rothberger's property. We apply these methods to construct a large family of spaces whose product with every Hurewicz space has Menger's property. Our applications extend earlier results of Babinkostova and Scheepers.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 03E17, 26A03, 03E75

Retrieve articles in all journals with MSC (2010): 03E17, 26A03, 03E75


Additional Information

Boaz Tsaban
Affiliation: Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel
Email: tsaban@math.biu.ac.il

Lyubomyr Zdomskyy
Affiliation: Kurt Gödel Research Center for Mathematical Logic, University of Vienna, Währinger Strasse 25, 1090 Vienna, Austria
Email: lzdomsky@logic.univie.ac.at

DOI: https://doi.org/10.1090/S0002-9939-2014-12012-0
Received by editor(s): May 30, 2012
Received by editor(s) in revised form: September 8, 2012
Published electronically: May 2, 2014
Communicated by: Julia Knight
Article copyright: © Copyright 2014 American Mathematical Society