The Closure and the Interior of C-convex Sets

Abstract

C-convexity of the closure, interiors and their lineal convexity are considered for C-convex sets under additional conditions of boundedness and nonempty interiors. The following questions on closure and the interior of C-convex sets were tackled 1. The closure of a bounded C-convex domain may not be lineally-convex. 2. The closure of a non-empty interior of a C-convex compact in Cn may not coincide with the original compact. 3. The interior of the closure of a bounded C-convex domain always coincides with the domain itself. The questions were formulated by Yu. B. Zelinsky