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MR2448596 54E35 (54F15 57M05 57N05)
Blokh, Alexander; Misiurewicz, Michał; Oversteegen, Lex Sets of constant distance from a compact set in 2-manifolds with a geodesic metric. Proc. Amer. Math. Soc. 137 (2009), no. 2, 733–743.
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