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A family of functors H_n(·) from the category of pairs of topological spaces and continuous maps, to the category of Abelian groups and group homomorphisms satisfies the ...

Let S be a nonempty set, then a filter on S is a nonempty collection F of subsets of S having the following properties: 1. emptyset not in F, 2. If A,B in F, then A ...

Let X and Y be Banach spaces and let f:X->Y be a function between them. f is said to be Gâteaux differentiable if there exists an operator T_x:X->Y such that, for all v in X, ...

Two topological spaces X and Y are homotopy equivalent if there exist continuous maps f:X->Y and g:Y->X, such that the composition f degreesg is homotopic to the identity ...

A linear system of equations is a set of n linear equations in k variables (sometimes called "unknowns"). Linear systems can be represented in matrix form as the matrix ...

Maxwell's equations are the system of partial differential equations describing classical electromagnetism and therefore of central importance in physics. In the so-called ...

A nilpotent Lie group is a Lie group G which is connected and whose Lie algebra is a nilpotent Lie algebra g. That is, its Lie algebra lower central series ...

Given a set X, a set function mu^*:2^X->[0,infty] is said to be an outer measure provided that mu^*(emptyset)=0 and that mu^* is countably monotone, where emptyset is the ...

Let (X,A,mu) and (Y,B,nu) be measure spaces, let R be the collection of all measurable rectangles contained in X×Y, and let lambda be the premeasure defined on R by ...

The spherical curve obtained when moving along the surface of a sphere with constant speed, while maintaining a constant angular velocity with respect to a fixed diameter ...