An infinite game with topological consequences

作者：Bell Jocelyn R^*

来源：Topology and Its Applications, 2014, 175: 1-14.

DOI：10.1016/j.topol.2014.06.014

• Topological game
• W-space
• Sigma-product

We introduce a two player infinite game for which a winning strategy is preserved by Sigma-products and implies the existence of a winning strategy in Gruenhage's W-space game. A space exhibiting a winning strategy is collectionwise normal and countably paracompact. Consequently, a Sigma-product of spaces is collectionwise normal if each space possesses a winning strategy. This is a generalization of a well-known result on Sigma-products of metrizable spaces. Finally we show certain uniform box products have a winning strategy. Published by Elsevier B.V.

• 出版日期2014-9-15