Lindelöf indestructibility, topological games and selection principles

• Autorzy: Marion Scheepers , Franklin D. Tall
• Języki publikacji: EN

Abstrakty

EN

Arhangel'skii proved that if a first countable Hausdorff space is Lindelöf, then its cardinality is at most $2^{ℵ₀}$. Such a clean upper bound for Lindelöf spaces in the larger class of spaces whose points are $G_{δ}$ 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.

Kategorie tematyczne

• 54D20: Noncompact covering properties (paracompact, Lindel\"of, etc.)
• 54A25: Cardinality properties (cardinal functions and inequalities, discrete subsets)
• 54A35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2010
• Tom: 210
• Numer: 1
• Strony: 1-46

Daty

wydano

2010

Twórcy

autor

Marion Scheepers

• Department of Mathematics, Boise State University, 1910 University Drive, Boise, ID 83725, U.S.A.

autor

Franklin D. Tall

• Department of Mathematics, University of Toronto, Toronto, Ontario M5S2E4, Canada

Identyfikatory

DOI

10.4064/fm210-1-1