ABSTRACT
A central concept in linear algebra is the idea of a subspace of a vector space. Subspaces provide an algebraic abstraction of “uncurved” geometric objects such as lines and planes through the origin in three-dimensional space. However, there are many other uncurved geometric figures that are not subspaces, including lines and planes not passing through the origin, individual points, line segments, triangles, quadrilaterals, polygons in the plane, tetrahedra, cubes, and solid polyhedra. The concepts of affine sets and convex sets provide an algebraic setting for studying such figures and their higher-dimensional analogues.
