A variation of the proximal infinite game

A variation of the proximal infinite game and a class of spaces more general than the proximal spaces are introduced. If the first player has a winning strategy in this variation then the space is pseudonormal. If the second player does not have a winning strategy then the space is an Arhangel'skii α2 space. This new version of the proximal game is used to show that a Σ-product of ω-bounded topological manifolds is pseudonormal.