Weak covering properties and infinite games
General Topology
2012-02-14 v2
Abstract
We investigate game-theoretic properties of selection principles related to weaker forms of the Menger and Rothberger properties. For appropriate spaces some of these selection principles are characterized in terms of a corresponding game. We use generic extensions by Cohen reals to illustrate the necessity of some of the hypotheses in our theorems.
Cite
@article{arxiv.1202.0194,
title = {Weak covering properties and infinite games},
author = {Liljana Babinkostova and Bruno A. Pansera and Marion Scheepers},
journal= {arXiv preprint arXiv:1202.0194},
year = {2012}
}
Comments
Version 2, 20 pages. Removed Theorem 21 of version 1, and replaced it with a reference to a counterexample for one of the two directions. Added an example of a non-Lindelof T_2 space for which TWO has a winning strategy in the almost Rothberger game. Added a diagram in the examples section to illustrate relations among the classes we consider