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On a measure space X, the set of square integrable L2-functions is an L^2-space. Taken together with the L2-inner product with respect to a measure mu, <f,g>=int_Xfgdmu (1) ...

The word polytope is used to mean a number of related, but slightly different mathematical objects. A convex polytope may be defined as the convex hull of a finite set of ...

A codimension one foliation F of a 3-manifold M is said to be taut if for every leaf lambda in the leaf space L of F, there is a circle gamma_lambda transverse to F (i.e., a ...

The algebraic identity (sum_(i=1)^na_ic_i)(sum_(i=1)^nb_id_i)-(sum_(i=1)^na_id_i)(sum_(i=1)^nb_ic_i) =sum_(1<=i<j<=n)(a_ib_j-a_jb_i)(c_id_j-c_jd_i). (1) Letting c_i=a_i and ...

The Wolfram Physics Project posits the existence of abstract relations between atoms of space whose pattern defines the structure of physical space. In this approach, two ...

The direct limit of the cohomology groups with coefficients in an Abelian group of certain coverings of a topological space.

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.

A Lie group is a smooth manifold obeying the group properties and that satisfies the additional condition that the group operations are differentiable. This definition is ...

Linear Algebra