Lindelöf indestructibility, topological games and selection principles

Marion Scheepers ¹   ; Franklin D. Tall ²

¹ Department of Mathematics Boise State University 1910 University Drive Boise, ID 83725, U.S.A.
² Department of Mathematics University of Toronto Toronto, Ontario M5S2E4, Canada

Fundamenta Mathematicae, Tome 210 (2010) no. 1, pp. 1-46

Résumé

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.

Détail

DOI : 10.4064/fm210-1-1

Keywords: arhangelskii proved first countable hausdorff space lindel its cardinality aleph clean upper bound lindel spaces larger class spaces whose points mathsf delta has elusive paper continue agenda started second author topology appl considering cardinality problem spaces satisfying stronger versions lindel property infinite games selection principles especially rothberger property essential tools investigations