The closure and the interior of $ \mathbb C$-convex sets

Sergej V. Znamenskij

Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 4, pp. 475-482.

Résumé

$ \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.

Détail

Keywords: strong linear convexity, $ \mathbb C $-convexity, projective convexity, lineal convexity, Fantappie transform, Aizenberg–Martineau duality.

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