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The adjective "affine" indicates everything that is related to the geometry of affine spaces. A coordinate system for the n-dimensional affine space R^n is determined by any ...

An alternating multilinear form on a real vector space V is a multilinear form F:V tensor ... tensor V->R (1) such that ...

The L^2-inner product of two real functions f and g on a measure space X with respect to the measure mu is given by <f,g>_(L^2)=int_Xfgdmu, sometimes also called the bracket ...

A collection of open sets of a topological space whose union contains a given subset. For example, an open cover of the real line, with respect to the Euclidean topology, is ...

A special nonsingular map from one manifold to another such that at every point in the domain of the map, the derivative is an injective linear transformation. This is ...

A skew conic, also known as a gauche conic, space conic, twisted conic, or cubical conic section, is a third-order space curve having up to three points in common with a ...

The set of projective projectively extended real numbers. Unfortunately, the notation is not standardized, so the set of affinely extended real numbers, denoted here R^_, is ...

A collection of subsets of a topological space that is contained in a basis of the topology and can be completed to a basis when adding all finite intersections of the ...

The set C_(n,m,d) of all m-D varieties of degree d in an n-dimensional projective space P^n into an M-D projective space P^M.

A set S is discrete in a larger topological space X if every point x in S has a neighborhood U such that S intersection U={x}. The points of S are then said to be isolated ...