Topology Vocabulary

Vocabulary
Here, a closed half-space is the half-space that includes the hyperplane.
 * Affine Space:"An affine space is a vector space that's forgotten its origin" (John Baez). In an affine space, one can subtract points to get vectors, or add a vector to a point to get another point, but one cannot add points. In particular, there is no distinguished point that serves as an origin.
 * Circumcircle:the circumscribed circle or circumcircle of a polygon is a circle which passes through all the vertices of the polygon. The centre of this circle is called the circumcenter.
 * Face:a face of a polyhedron is any of the polygons that make up its boundaries. For example, any of the squares that bound a cube is a face of the cube. In convex geometry, a face of a polytope P is the intersection of any supporting hyperplane of P and P. From this definition it follows that the set of faces of a polytope includes the polytope itself and the empty set. For example, a polyhedron R3 is entirely on one hyperplane of R4. If R4 were spacetime, the hyperplane at t=0 supports and contains the entire polyhedron. Thus, by the formal definition, the polyhedron is a face of itself.
 * Facet:A facet of an n-polytope is an (n-1)-dimensional face or (n-1)-face. For example:
 * The facets of a polygon are edges. (1-faces)
 * The facets of a polyhedron are faces. (2-faces)
 * The facets of a polychoron (4-polytope) are cells. (3-faces)
 * The facets of a polyteron (5-polytope) are hypercells. (4-faces)
 * Hyperplane:It is a higher-dimensional generalization of the concepts of a line in Euclidean plane geometry and a plane in 3-dimensional Euclidean geometry.
 * Polytope:Polytope means, first, the generalization to any dimension of polygon in two dimensions, polyhedron in three dimensions, and polychoron in four dimensions.
 * Simplex:In geometry, a simplex (plural simplexes or simplices) or n-simplex is an n-dimensional analogue of a triangle. Specifically, a simplex is the convex hull of a set of (n + 1) affinely independent points in some Euclidean space of dimension n or higher. For example, a 0-simplex is a point, a 1-simplex is a line segment, a 2-simplex is a triangle, a 3-simplex is a tetrahedron, and a 4-simplex is a pentachoron (in each case with interior).
 * Supporting Hyperplane: A hyperplane divides a space into two half-spaces. A hyperplane is said to support a set S in Euclidean space \mathbb R^n if it meets both of the following:
 * S is entirely contained in one of the two closed half-spaces of the hyperplane
 * S has at least one point on the hyperplane
 * Triangulation:a subdivision of a geometric object into simplices. In particular, in the plane it is a subdivision into triangles,

Topology

 * O.Viro, O.Ivanov, V.Kharlamov, N.Netsvetaev: Elementary Topology
 * Wikipedia: Topology Glossary
 * Michael Garland's Papers