Geodesic
On the $P$-Property of Compact Convex Sets
Matematičeskie zametki, Tome 71 (2002) no. 3, pp. 323-333

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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. 
@article{MZM_2002_71_3_a0,
     author = {M. V. Balashov},
     title = {On the $P${-Property} of {Compact} {Convex} {Sets}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {323--333},
     publisher = {mathdoc},
     volume = {71},
     number = {3},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_71_3_a0/}
}
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M. V. Balashov. On the $P$-Property of Compact Convex Sets. Matematičeskie zametki, Tome 71 (2002) no. 3, pp. 323-333. http://geodesic.mathdoc.fr/item/MZM_2002_71_3_a0/