Mathematical Logic Quarterly 59 (1-2):101-107 (2013)

Abstract
Sufficient conditions are given for the computation of an arc that accesses a point on the boundary of an open subset of the plane from a point within the set. The existence of a not-computably-accessible but computable point on a computably compact arc is also demonstrated
Keywords 30C30  30C85  MSC (2010) 03F60  Computable topology  effective local connectivity  30C20
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DOI 10.1002/malq.201200026
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Effective Borel Measurability and Reducibility of Functions.Vasco Brattka - 2005 - Mathematical Logic Quarterly 51 (1):19-44.

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