  Properties of two classes of generally convex sets in the n-dimentional real
Euclidean space, called m-semiconvex and weakly m-semiconvex, 1<=m<n, are
investigated in the present work. In particular, it is established that an open
set with smooth boundary in the plan which is weakly 1-semiconvex but not
1-semiconvex consists minimum of four simply connected components.
