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The Lebesgue covering dimension is an important dimension and one of the first dimensions investigated. It is defined in terms of covering sets, and is therefore also called ...

Given an m×n matrix A, the fundamental theorem of linear algebra is a collection of results relating various properties of the four fundamental matrix subspaces of A. In ...

Let M be a Riemannian manifold, and let the topological metric on M be defined by letting the distance between two points be the infimum of the lengths of curves joining the ...

The compound of the snub cube and its dual, the pentagonal icositetrahedron. Surprisingly, the tribonacci constant t is intimately related to the metric properties of the ...

The Weyl tensor is the tensor C_(abcd) defined by R_(abcd)=C_(abcd)+2/(n-2)(g_(a[c)R_d]b-g_(b[c)R_(d]a)) -2/((n-1)(n-2))Rg_(a[c)g_(d]b), (1) where R_(abcd) is the Riemann ...

Two distinct theorems are referred to as "the de Bruijn-Erdős theorem." One of them (de Bruijn and Erdős 1951) concerns the chromatic number of infinite graphs; the other (de ...

An iterated fibration of Eilenberg-Mac lane spaces. Every topological space has this homotopy type.

Gauss's theorema egregium states that the Gaussian curvature of a surface embedded in three-space may be understood intrinsically to that surface. "Residents" of the surface ...

Oriented spheres in complex Euclidean three-space can be represented as lines in complex projective three-space ("Lie correspondence"), and the spheres may be thought of as ...

A property that passes from a topological space to all its quotient spaces. This is true for connectedness, local connectedness and separability, but not for any of the ...