Covering properties on X2⧹Δ, W-sets, and compact subsets of Σ-products

AbstractLet Δ ⊂ X1 be the diagonal. In the first part of this paper, we show that a compact space X is Corson compact (resp., Eberlein compact; compact metric) if and only if X2⧹Δ is metalindelöf (resp., σ-metacompact; paracompact). In the second part of the paper, we investigate the notion of a W-set in a space X, which is defined in terms of an infinite game. We show that a compact space X is Corson compact if and only if X has a W-set diagonal, and that a compact scattered space X is strong Eberlein compact if and only if each point of X is a W-set in X