On prime ends and local connectivity | Zendy

Rempe Lasse | Zendy

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On prime ends and local connectivity

Author(s) -

Rempe Lasse

Publication year - 2008

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1112/blms/bdn061

Subject(s) - mathematics , complement (music) , prime (order theory) , characterization (materials science) , combinatorics , point (geometry) , domain (mathematical analysis) , discrete mathematics , geometry , mathematical analysis , physics , biochemistry , chemistry , complementation , optics , gene , phenotype

Let U ⊂ ℂ̂ be a simply connected domain whose complement K = ℂ̂∖ U contains more than one point. We show that the impression of a prime end of U contains at most two points at which K is locally connected. This is achieved by establishing a characterization of local connectivity of K at a point z 0 ∈ ∂ U in terms of the prime ends of U whose impressions contain z 0 , and then invoking a result of Ursell and Young.

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