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- W2017294851 abstract "We present several results on compact Hausdorff spaces which can be represented as unions of nice subspaces. Some typical results are: If X is a compact Hausdorff space, and X = ∪α<κXα, where each Xα is κ-refinable and Ψ(Xα) ⩽ κ, then (i) every nonempty Gκ-subset of X contains a point of character ⩽κ, (ii) if xϵX, χ(x, X) = μ > κ and μ is regular, then there exists a discrete sequence {xα: α<μ} in X such that xα→x, (iii) if A is a nonclosed subset of X, then there exists a point x ϵ XA and a filter base F of subsets of A such that | F | ⩽κ and F→x. We also show that if a compact Hausdorff space X is a union of countably many metrizable spaces, X has no isolated points and c(X)=ω0, then X is a compactification of the space of irrationals." @default.
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- W2017294851 date "1994-10-01" @default.
- W2017294851 modified "2023-10-17" @default.
- W2017294851 title "Compact spaces representable as unions of nice subspaces" @default.
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- W2017294851 doi "https://doi.org/10.1016/0166-8641(94)90025-6" @default.
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