Abstract: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 Lindel\"of spaces are shown.
Keywords: topological game, network, netweight, weakly separated, $D$-space
AMS Subject Classification: 54D20 54E20