Separating by $G_{δ}$-sets in finite powers of ω₁

• Autorzy: Yasushi Hirata , Nobuyuki Kemoto
• Języki publikacji: EN

Abstrakty

EN

It is known that all subspaces of ω₁² have the property that every pair of disjoint closed sets can be separated by disjoint $G_{δ}$-sets (see [4]). It has been conjectured that all subspaces of ω₁ⁿ also have this property for each n < ω. We exhibit a subspace of {⟨α,β,γ⟩ ∈ ω₁³: α ≤ β ≤ γ} which does not have this property, thus disproving the conjecture. On the other hand, we prove that all subspaces of {⟨α,β,γ⟩ ∈ ω₁³: α < β < γ} have this property.

Kategorie tematyczne

• 54B10: Product spaces
• 54D20: Noncompact covering properties (paracompact, Lindel\"of, etc.)
• 03E10: Ordinal and cardinal numbers
• 54D15: Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2003
• Tom: 177
• Numer: 1
• Strony: 83-94

Daty

wydano

2003

Twórcy

autor

Yasushi Hirata

• Graduate School of Mathematics, University of Tsukuba, Ibaraki 305-8571, Japan

autor

Nobuyuki Kemoto

• Department of Mathematics, Faculty of Education, Oita University, Dannoharu, Oita, 870-1192, Japan

Identyfikatory

DOI

10.4064/fm177-1-5