Lindelöf indestructibility, topological games and selection principles

Volume 210 / 2010

Marion Scheepers, Franklin D. Tall Fundamenta Mathematicae 210 (2010), 1-46 MSC: 54A25, 54A35, 54D20. DOI: 10.4064/fm210-1-1

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 $\mathsf G_{\delta }$ 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.

Authors

  • Marion ScheepersDepartment of Mathematics
    Boise State University
    1910 University Drive
    Boise, ID 83725, U.S.A.
    e-mail
  • Franklin D. TallDepartment of Mathematics
    University of Toronto
    Toronto, Ontario M5S2E4, Canada
    e-mail

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