International Conference
"Modern Problems of Mathematics, Informatics and Bioinformatics",
devoted to the 100th anniversary of professor Alexei A. Lyapunov

Novosibirsk, Russia, 2011, October 11-14

Кутателадзе С.С.  

Convexity and Inequality

Linear inequality implies linearity and order. When combined, the two produce an ordered vector space. Each linear inequality in the simplest environment of the sort is some half-space. Simultaneity implies many instances and so leads to the intersections of half-spaces. These yield polyhedra as well as arbitrary convex sets, identifying the theory of linear inequalities with convexity.