Stone's separation theorem #
This file proves Stone's separation theorem. This tells us that any two disjoint convex sets can be separated by a convex set whose complement is also convex.
In locally convex real topological vector spaces, the Hahn-Banach separation theorems provide stronger statements: one may find a separating hyperplane, instead of merely a convex set whose complement is convex.
In a tetrahedron with vertices
q, any segment
[u, v] joining the opposite
[x, p] and
[y, q] passes through any triangle of vertices
z ∈ [x, y].