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The unit lower half-disk is the portion of the complex plane satisfying {|z|<=1,I[z]<0}.

The unit upper half-disk is the portion of the complex plane satisfying {|z|<=1,I[z]>0}.

In functional analysis, the Banach-Alaoglu theorem (also sometimes called Alaoglu's theorem) is a result which states that the norm unit ball of the continuous dual X^* of a ...

The Riemann sphere, also called the extended complex plane, is a one-dimensional complex manifold C^* (C-star) which is the one-point compactification of the complex numbers ...

The geometry of Finsler space.

A space having dimension n>3.

An algorithm for finding roots for quartic equations with complex roots.

In the archaic terminology of Whittaker and Watson (1990), the complex number z representing x+iy.

A continuous transformation from one function to another. A homotopy between two functions f and g from a space X to a space Y is a continuous map G from X×[0,1]|->Y such ...

The space of continuously differentiable functions is denoted C^1, and corresponds to the k=1 case of a C-k function.