2013/10/31 by Arnold W. Miller, Boaz Tsaban, Lyubomyr Zdomskyy · 1 citation
Mathematics · #math.FA #math.GN #math.LO
paper · pdf · doi:10.1090/tran/6581
published as Transactions of the American Matheamtical Society 368 (2016), 2865-2889 · Minor errors corrected
arxiv created 2018/10/10 · arxiv updated 2018/10/11
We study productive properties of gamma spaces, and their relation to other, classic and modern, selective covering properties. Among other things, we prove the following results: 1. Solving a problem of F. Jordan, we show that for every unbounded tower set of reals X of cardinality aleph1, the space Cp(X) is productively FU. In particular, the set X is productively gamma. 2. Solving problems of Scheepers and Weiss, and proving a conjecture of Babinkostova-Scheepers, we prove that, assuming CH, there are gamma spaces whose product is not even Menger. 3. Solving a problem of Scheepers-Tall, we show that the properties gamma and Gerlits--Nagy (*) are preserved by Cohen forcing. Moreover, every Hurewicz space that Remains Hurewicz in a Cohen extension must be Rothberger (and thus (*)). We apply our results to solve a large number of additional problems, and use Arhangel'skii duality to obtain results concerning local properties of function spaces and countable topological groups.