Compactness and symmetric well-orders

• Autorzy: Dasgupta Abhijit

Identyfikatory

DOI

10.4064/ba230424-28-12

• Języki publikacji: EN

Abstrakty

EN

We introduce and investigate a topological form of Stäckel’s 1907 characterization of finite sets, with the goal of obtaining an interesting notion that characterizes usual compactness (or a close variant of it). Define a T2 topological space (X,τ) to be Stäckel-compact if there is some linear ordering ≺ on X such that every non-empty τ-closed set contains a ≺-least and a ≺-greatest element. We find that compact spaces are Stäckel-compact but not conversely, and Stäckel-compact spaces are countably compact. The equivalence of Stäckel-compactness with countable compactness remains open, but our main result is that this equivalence holds in scattered spaces of Cantor–Bendixson rank <ω2 under ZFC. Under V=L, the equivalence holds in all scattered spaces.

Słowa kluczowe

EN

compactness; well-order; Cantor–Bendixson

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2024
• Tom: Vol. 72, no 1
• Strony: 67--80
• Opis fizyczny: Bilbiogr. 8 poz.

Twórcy

autor

Dasgupta Abhijit

• Department of Mathematics, University of Detroit Mercy, Detroit, MI 48221, USA

Bibliografia

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