Abstract
Let S be a compact set in R 2. For S simply connected, S is a union of two starshaped sets if and only if for every F finite, F \( \subseteq \) bdry S, there exist a set G \( \subseteq \) bdry S arbitrarily close to F and points s, t depending on G such that each point of G is clearly visible via S from one of s, t. In the case where ∼S has at most finitely many components, the necessity of the condition still holds while the sufficiency fails.
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Breen, M., Zamfirescu, T. A characterization theorem for certain unions of two starshaped sets in R 2 . Geom Dedicata 22, 95–103 (1987). https://doi.org/10.1007/BF00183056
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DOI: https://doi.org/10.1007/BF00183056