Geodesic
The closure and the interior of $ \mathbb C$-convex sets
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 4, pp. 475-482

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$ \mathbb C $-convexity of the closure, interiors and their lineal convexity are considered for $ \mathbb C $-convex sets under additional conditions of boundedness and nonempty interiors. The following questions on closure and the interior of $\mathbb C $-convex sets were tackled The closure of a bounded $ \mathbb C $-convex domain may not be lineally-convex.    The closure of a non-empty interior of a $ \mathbb C $-convex compact in $ \mathbb C^n $ may not coincide with the original compact. The interior of the closure of a bounded $ \mathbb C $-convex domain always coincides with the domain itself. The questions were formulated by Yu. B. Zelinsky.
Keywords: strong linear convexity, $ \mathbb C $-convexity, projective convexity, lineal convexity, Fantappie transform, Aizenberg–Martineau duality. 
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     author = {Sergej V. Znamenskij},
     title = {The closure and the interior of $ \mathbb C$-convex sets},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {475--482},
     publisher = {mathdoc},
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     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2019_12_4_a9/}
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Sergej V. Znamenskij. The closure and the interior of $ \mathbb C$-convex sets. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 4, pp. 475-482. http://geodesic.mathdoc.fr/item/JSFU_2019_12_4_a9/