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A continuous map is a continuous function between two topological spaces. In some fields of mathematics, the term "function" is reserved for functions which are into the real ...

The region 0<sigma<1, where sigma is defined as the real part of a complex number s=sigma+it. All nontrivial zeros (i.e., those not at negative even integers) of the Riemann ...

On the Clebsch diagonal cubic, all 27 of the complex lines present on a general smooth cubic surface are real. In addition, there are 10 points on the surface where three of ...

A collection of faces of an n-dimensional polytope or simplicial complex, one of each dimension 0, 1, ..., n-1, which all have a common nonempty intersection. In normal three ...

Functional analysis is a branch of mathematics concerned with infinite-dimensional vector spaces (mainly function spaces) and mappings between them. The spaces may be of ...

Let C denote a chain complex, a portion of which is shown below: ...->C_(n+1)->C_n->C_(n-1)->.... Let H_n(C)=kerpartial_n/Impartial_(n+1) denotes the nth homology group. Then ...

An n×n complex matrix A is called indefinite if nonzero vectors x and y exist such that x^*Ax>0>y^*Ay, where x^* denotes the conjugate transpose. A matrix m may be tested to ...

An isogonal mapping is a transformation w=f(z) that preserves the magnitudes of local angles, but not their orientation. A few examples are illustrated above. A conformal ...

Given a matrix A, a Jordan basis satisfies Ab_(i,1)=lambda_ib_(i,1) and Ab_(i,j)=lambda_ib_(i,j)+b_(i,j-1), and provides the means by which any complex matrix A can be ...

A finitely generated discontinuous group of linear fractional transformations z->(az+b)/(cz+d) acting on a domain in the complex plane. The Apollonian gasket corresponds to a ...