Lindelöf indestructibility, topological games and selection principles
Tom 210 / 2010
Fundamenta Mathematicae 210 (2010), 1-46
MSC: 54A25, 54A35, 54D20.
DOI: 10.4064/fm210-1-1
Streszczenie
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 $\mathsf G_{\delta }$ has been more elusive. In this paper we continue the agenda started by the second author, [Topology Appl. 63 (1995)], 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.
