Lindelöf indestructibility, topological games and selection principles

Marion Scheepers, and Franklin D. Tall. "Lindelöf indestructibility, topological games and selection principles." Fundamenta Mathematicae 210.1 (2010): 1-46. <http://eudml.org/doc/283020>.

@article{MarionScheepers2010,
abstract = {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.},
author = {Marion Scheepers, Franklin D. Tall},
journal = {Fundamenta Mathematicae},
keywords = {Lindelöf spaces; Rothberger Property; indestructibly Lindelöf spaces; topological games; selection properties; Hurewicz property; Menger property; Gerlits-Nagy property},
language = {eng},
number = {1},
pages = {1-46},
title = {Lindelöf indestructibility, topological games and selection principles},
url = {http://eudml.org/doc/283020},
volume = {210},
year = {2010},
}

TY - JOUR
AU - Marion Scheepers
AU - Franklin D. Tall
TI - Lindelöf indestructibility, topological games and selection principles
JO - Fundamenta Mathematicae
PY - 2010
VL - 210
IS - 1
SP - 1
EP - 46
AB - 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.
LA - eng
KW - Lindelöf spaces; Rothberger Property; indestructibly Lindelöf spaces; topological games; selection properties; Hurewicz property; Menger property; Gerlits-Nagy property
UR - http://eudml.org/doc/283020
ER -