On the $P$-Property of Compact Convex Sets

Compact convex sets with a special property ($P$-property) in a finite-dimensional space are considered. This property ensures a certain regularity of the boundaries of such sets. A fairly complete description of the class of compact convex sets with the $P$-property is given. It is shown that this class is closed with respect to the basic set operations. The application of the $P$-property is exemplified; in particular, it is shown that any generating set has the $P$-property.