Games, covering properties and Eberlein compacts (Q1083060)

The following topological game is studied on a locally compact space X: at the nth move, Player K chooses a compact set \(K_ n\subset X\), and Player P chooses a point \(p_ n\not\in \{K_ i:\) \(i\leq n\}\). Player K wins the play if \(\{p_ n:\) \(n<\omega \}\) has no limit point in X. It is shown that X is metacompact (resp. \(\sigma\)-metacompact) iff Player K has a stationary (resp. Markov) winning strategy in the game. From this statement follows a game-theoretic characterization of Eberlein compacta. If Player P is allowed to choose compact sets instead od points, then Player K has a winning strategy iff X is paracompact.