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If f:M->N, then the tangent map Tf associated to f is a vector bundle homeomorphism Tf:TM->TN (i.e., a map between the tangent bundles of M and N respectively). The tangent ...

The tilde is the mark "~" placed on top of a symbol to indicate some special property. x^~ is voiced "x-tilde." The tilde symbol is commonly used to denote an operator. In ...

A continuous group G which has the topology of a T2-space is a topological group. The simplest example is the group of real numbers under addition. The homeomorphism group of ...

In the American system, one trillion equals 10^(12)=1000000000000. In the French and German systems, one trillion equals 10^(18). In recent years, the "American" system has ...

A finite simple group of Lie-type. The following table summarizes the types of twisted Chevalley groups and their respective orders. In the table, q denotes a prime power and ...

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 graph for which the relations between pairs of vertices are symmetric, so that each edge has no directional character (as opposed to a directed graph). Unless otherwise ...

A square matrix A is said to be unipotent if A-I, where I is an identity matrix is a nilpotent matrix (defined by the property that A^n is the zero matrix for some positive ...

The vierergruppe is the Abelian abstract group on four elements that is isomorphic to the finite group C2×C2 and the dihedral group D_2. The multiplication table of one ...

A number n is called wasteful if the number of digits in the prime factorization of n (including powers) uses more digits than the number of digits in n. The first few ...