3Polytopes, positive bases, and inequality systems
In this chapter, we study some combinatorial and structural properties of convex polytopes, positive bases of vector spaces, and infeasible systems of linear inequalities.
It was shown in the previous chapters that infeasible systems of linear inequalities inherit their significant properties from other fundamental mathematical constructions. For example, being infeasible systems with the monotonicity property, systems of linear inequalities can additionally be described in the language of abstract simplicial complexes. The connectedness of the graphs of maximal feasible subsystems of such systems follows from the fundamental topological property of the connectedness of the space R n.