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

$ \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.