The interior structure and compactness of B-convex hull

Based on the definition of B-convex set, which was introduced by Bector etc. via loosening the convexity of convex set (Bector, CR, et al., 1991 and 1993), the definition of B-convex set is given and the interior structure is discussed. In the meantime, an important topological property of B-convex set, i.e. the compactness of B-convex set, is given.