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

In a chain complex of modules ...->C_(i+1)->^(d_(i+1))C_i->^(d_i)C_(i-1)->... the module Z_i of i-cycles is the kernel of d_i, which is a submodule of C_i.

Let K be a finite complex, let h:|K|->|K| be a continuous map. If Lambda(h)!=0, then h has a fixed point.

An algorithm which isolates roots in the complex plane by generalizing one-dimensional bracketing.

Let y_n be a complex number for 1<=n<=N and let y_n=0 if n<1 or n>N. Then (Montgomery 2001).

A complex manifold for which the exterior derivative of the fundamental form Omega associated with the given Hermitian metric vanishes, so dOmega=0. In other words, it is a ...

A gadget defined for complex vector bundles. The Chern classes of a complex manifold are the Chern classes of its tangent bundle. The ith Chern class is an obstruction to the ...

In a cochain complex of modules ...->C^(i-1)->^(d^(i-1))C^i->^(d^i)C^(i+1)->..., the module B^i of i-coboundaries is the image of d^(i-1). It is a submodule of C^i and is ...

The operator partial^_ is defined on a complex manifold, and is called the 'del bar operator.' The exterior derivative d takes a function and yields a one-form. It decomposes ...

A directed infinity in direction z is an infinite numerical quantity that is a positive real multiple of the complex number z. Directed infinity may be returned in the ...