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A measure which takes values in the complex numbers. The set of complex measures on a measure space X forms a vector space. Note that this is not the case for the more common ...

A set S in a vector space over R is called a convex set if the line segment joining any pair of points of S lies entirely in S.

The plane spanned by two coordinate axes in the three-dimensional Euclidean space. The coordinate plane spanned by the x- and the y-axis is called xy-plane.

The cotangent bundle of a manifold is similar to the tangent bundle, except that it is the set (x,f) where x in M and f is a dual vector in the tangent space to x in M. The ...

The n-cyclohedron, also known as the Bott-Taubes polytope, is defined as the compactification of the configuration space of n points on the circle. The cyclohedron can be ...

Given a vector bundle pi:E->M, its dual bundle is a vector bundle pi^*:E^*->M. The fiber bundle of E^* over a point p in M is the dual vector space to the fiber of E.

One of the Eilenberg-Steenrod axioms which states that, if X is a space with subspaces A and U such that the set closure of A is contained in the interior of U, then the ...

Any nondegenerate closed space curve may be nondegenerately deformed into either of the two curves illustrated above. Neither of these can be nondegenerately transformed into ...

In elliptic n-space, the pole of an (n-1)-flat is a point located at an arc length of pi/2 radians away from each point of the (n-1)-flat.

If it is possible to transform a coordinate system to a form where the metric elements g_(munu) are constants independent of x^mu, then the space is flat.