Half-space
= Half-space
{title2=$\{x:a^Tx\le b\},\quad a\ne0$}
A closed half-space consists of a <hyperplane> and one of its two sides in a real <affine space>. Replacing the weak inequality by a strict inequality gives an open half-space. Half-spaces are <convex sets>, and finite <intersections> of closed <half-spaces> are <linear polyhedra>.