Geodesic
Uniform Approximation by Meromorphic Functions on Closed Sets with Continuous extension into the Boundary
Canadian journal of mathematics, Tome 30 (1978) no. 6, pp. 1243-1255

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Notation. For S a subset of the extended plane C* = C ∪ (∞ ) let S0 be its interior, its closure in C* and its boundary. H(S) and M(S) will denote the sets of all restrictions to S of functions which are, on a neighborhood of S, holomorphic or meromorphic, respectively. A (S) will stand for the set of functions from S to C* which are continuous on S and whose restriction to S° are holomorphic. 
Uniform Approximation by Meromorphic Functions on Closed Sets with Continuous extension into the Boundary. Canadian journal of mathematics, Tome 30 (1978) no. 6, pp. 1243-1255. doi: 10.4153/CJM-1978-103-4
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