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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 ...

A nonlinear deconvolution technique used in deconvolving images from the Hubble Space Telescope before corrective optics were installed.

An n-dimensional vector, i.e., a vector (x_1, x_2, ..., x_n) with n components. In dimensions n greater than or equal to two, vectors are sometimes considered synonymous with ...

If a subgroup H of G has a group representation phi:H×W->W, then there is a unique induced representation of G on a vector space V. The original space W is contained in V, ...

A subset {v_1,...,v_k} of a vector space V, with the inner product <,>, is called orthogonal if <v_i,v_j>=0 when i!=j. That is, the vectors are mutually perpendicular. Note ...

In functional analysis, the Banach-Alaoglu theorem (also sometimes called Alaoglu's theorem) is a result which states that the norm unit ball of the continuous dual X^* of a ...

A manifold with a Riemannian metric that has zero curvature is a flat manifold. The basic example is Euclidean space with the usual metric ds^2=sum_(i)dx_i^2. In fact, any ...

The hyperbolic polar sine is a function of an n-dimensional simplex in hyperbolic space. It is analogous to the polar sine of an n-dimensional simplex in elliptic or ...

A convex body in Euclidean space that is centrally symmetric with center at the origin is determined among all such bodies by its brightness function (the volume of each ...

A weakened version of pointwise convergence hypothesis which states that, for X a measure space, f_n(x)->f(x) for all x in Y, where Y is a measurable subset of X such that ...