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- W2106942452 abstract "We prove that, assuming MA, every crowded T0 space X is ω-resolvable if it satisfies one of the following properties: (1) it contains a π-network of cardinality < c constituted by infinite sets, (2) χ(X) < c, (3) X is a T2 Baire space and c(X) ≤ ℵ0 and (4) X is a T1 Baire space and has a network N with cardinality < c and such that the collection of the finite elements in it constitutes a σ-locally finite family. Furthermore, we prove that the existence of a T1 Baire irresolvable space is equivalent to the existence of a T1 Baire ω-irresolvable space, and each of these statements is equivalent to the existence of a T1 almost-ω-irresolvable space. Finally, we prove that the minimum cardinality of a π-network with infinite elements of a space Seq(ut) is strictly greater than ℵ0." @default.
- W2106942452 created "2016-06-24" @default.
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- W2106942452 date "2009-01-01" @default.
- W2106942452 modified "2023-09-24" @default.
- W2106942452 title "MARTIN'S AXIOM AND !-RESOLVABILITY OF BAIRE SPACES" @default.
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