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arXiv · 0902.1944

Lindelof indestructibility, topological games and selection principles

Marion Scheepers·Franklin D. Tall
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Abstract

Arhangel'skii proved that if a first countable Hausdorff space is Lindelöf, then its cardinality is at most $2^{\aleph_0}$. Such a clean upper bound for Lindelöf spaces in the larger class of spaces whose points are ${\sf G}_δ$ has been more elusive. In this paper we continue the agenda started in F.D. Tall, On the cardinality of Lindelöf spaces with points $G_δ$, Topology and its Applications 63 (1995), 21 - 38, of considering the cardinality problem for spaces satisfying stronger versions of the Lindelöf property. Infinite games and selection principles, especially the Rothberger property, are essential tools in our investigations

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Marion Scheepers, Franklin D. Tall. 2009-09-02. Lindelof indestructibility, topological games and selection principles. https://arxiv.org/abs/0902.1944

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