Timothy H. McNicholl
Abstract
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It is shown that there is a computable conformal map of the unit disk onto a domain $D$ that has a computable extension to the closure of the unit disk even though the boundary of $D$ is not effectively locally connected. The proof encodes an arbitrary \emph{c.e.} set into the local connectivity of the boundary of $D$.
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It is shown that there is a computable conformal map of the unit disk onto a domain $D$ that has a computable extension to the closure of the unit disk even though the boundary of $D$ is not effectively locally connected. The proof encodes an arbitrary \emph{c.e.} set into the local connectivity of the boundary of $D$.
Key concepts: Unit disk, Conformal map, Boundary (topology), Extension (predicate logic), Closure (psychology), Domain (mathematical analysis), Unit (ring theory), Set (abstract data type)