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- W4210847541 abstract "Let j:Y→X be a continuous surjection of compact metric spaces. Whyburn proved that j is irreducible, meaning that j(F)⊊X for any proper closed subset F⊊Y, if and only if j is almost one-to-one, in the sense that{y∈Y:card(j−1(j(y)))=1}‾=Y. In this note we prove the following generalization: There exists a unique minimal closed set K⊆Y such that j(K)=X if and only if{x∈X:card(j−1(x))=1}‾=X. Translated to the language of operator algebras, this says that if A⊆B is a unital inclusion of separable abelian C⁎-algebras, then there exists a unique pseudo-expectation (in the sense of Pitts) if and only if the almost extension property of Nagy-Reznikoff holds. More generally, we prove that a unital inclusion of (not necessarily separable) abelian C⁎-algebras has a unique pseudo-expectation if and only if it is aperiodic (in the sense of Kwaśniewski-Meyer)." @default.
- W4210847541 created "2022-02-09" @default.
- W4210847541 creator A5030520218 @default.
- W4210847541 date "2022-04-01" @default.
- W4210847541 modified "2023-10-17" @default.
- W4210847541 title "A generalization of Whyburn's theorem, and aperiodicity for Abelian C⁎-inclusions" @default.
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- W4210847541 doi "https://doi.org/10.1016/j.topol.2022.108043" @default.
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