Abstract
We prove that if X is a compact T2 space (and x ε{lunate} X) and π(X)=κ (πχ(x, X)=κ), then there is a dense subset Y ⊂ X (resp. a set Y ⊂ X with x ε{lunate} Ȳ) such that d(Y)=κ (resp. x∉Z̄ for any Z ⊂ Y with |Z|<κ). Previously this only has been proven for κ regular. A consequence is that the point-picking game GD α(X) is always determined if X is compact T2.
Original language | English |
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Pages (from-to) | 289-294 |
Number of pages | 6 |
Journal | Topology and its Applications |
Volume | 32 |
Issue number | 3 |
DOIs | |
State | Published - Aug 1989 |
Keywords
- Boolean algebra of regular open subsets
- compact
- dense set
- point-picking game
- singular cardinals
- π-weight