Geodesic
A game and its relation to netweight and D-spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 52 (2011) no. 4, pp. 561-568.

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We introduce a two player topological game and study the relationship of the existence of winning strategies to base properties and covering properties of the underlying space. The existence of a winning strategy for one of the players is conjectured to be equivalent to the space have countable network weight. In addition, connections to the class of D-spaces and the class of hereditarily Lindelöf spaces are shown.
Classification : 54D20, 54E20
Keywords: topological game; network; netweight; weakly separated; $D$-space 
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Gruenhage, Gary; Szeptycki, Paul. A game and its relation to netweight and D-spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 52 (2011) no. 4, pp. 561-568. http://geodesic.mathdoc.fr/item/CMUC_2011__52_4_a7/