Calibres, compacta and diagonals

• Autorzy: Paul Gartside , Jeremiah Morgan
• Języki publikacji: EN

Abstrakty

EN

For a space Z let 𝒦(Z) denote the partially ordered set of all compact subspaces of Z under set inclusion. If X is a compact space, Δ is the diagonal in X², and 𝒦(X²∖Δ) has calibre (ω₁,ω), then X is metrizable. There is a compact space X such that X²∖Δ has relative calibre (ω₁,ω) in 𝒦(X²∖Δ), but which is not metrizable. Questions of Cascales et al. (2011) concerning order constraints on 𝒦(A) for every subspace of a space X are answered.

Kategorie tematyczne

• 54E35: Metric spaces, metrizability
• 54D30: Compactness
• 54G20: Counterexamples

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2016
• Tom: 232
• Numer: 1
• Strony: 1-19

Daty

wydano

2016

Twórcy

autor

Paul Gartside

• Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, U.S.A.

autor

Jeremiah Morgan

• Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, U.S.A.

Identyfikatory

DOI

10.4064/fm232-1-1