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JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 2002 Volume 71, Issue 3, Pages 323–333 (Mi mzm349)

This article is cited in 11 papers

On the $P$-Property of Compact Convex Sets

M. V. Balashov

Moscow Institute of Physics and Technology

Abstract: 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.

UDC: 517.977.8

Received: 22.11.2000
Revised: 04.10.2001

DOI: 10.4213/mzm349


 English version:
Mathematical Notes, 2002, 71:3, 295–304

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© Steklov Math. Inst. of RAS, 2025