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A topological space fulfilling the T_2-axiom: i.e., any two points have disjoint neighborhoods. In the terminology of Alexandroff and Hopf (1972), a T_2-space is called a ...

The Riemann sphere C^*=C union {infty}, also called the extended complex plane. The notation C^^ is sometimes also used (Krantz 1999, p. 82). The notation C^* is also used to ...

There are two possible definitions: 1. Possessing similarity of form, 2. Continuous, one-to-one, in surjection, and having a continuous inverse. The most common meaning is ...

The study of the geometry of figures by algebraic representation and manipulation of equations describing their positions, configurations, and separations. Analytic geometry ...

The Kähler potential is a real-valued function f on a Kähler manifold for which the Kähler form omega can be written as omega=ipartialpartial^_f. Here, the operators ...

A Hermitian metric on a complex vector bundle assigns a Hermitian inner product to every fiber bundle. The basic example is the trivial bundle pi:U×C^k->U, where U is an open ...

Each of the maps of a cochain complex ...->C^(i-1)->^(d^(i-1))C^i->^(d^i)C^(i+1)->... is known as a coboundary operator.

In a cochain complex of modules ...->C^(i-1)->^(d^(i-1))C^i->^(d^i)C^(i+1)->... the module Z^i of i-cocycles Z^i is the kernel of d^i, which is a submodule of C^i.

A connection defined on a smooth algebraic variety defined over the complex numbers.

If A is a unital Banach algebra where every nonzero element is invertible, then A is the algebra of complex numbers.