On Prime Ends and Local Connectivity
نویسندگان
چکیده
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 z0 ∈ ∂U in terms of the prime ends of U whose impressions contain z0 and then invoking a result of Ursell and Young [UY].
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