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Four-dimensional geometry is Euclidean geometry extended into one additional dimension. The prefix "hyper-" is usually used to refer to the four- (and higher-) dimensional ...

In the algebraic geometry of Grothendieck, a stack refers to a sheaf of categories. In particular, a stack is a presheaf of categories in which the following descent ...

Any collineation from P(V) to P(V), where V is a three-dimensional vector space, is associated with a semilinear map from V to V.

On a Riemannian manifold, there is a unique connection which is torsion-free and compatible with the metric. This connection is called the Levi-Civita connection.

A synonym for analytic function, regular function, differentiable function, complex differentiable function, and holomorphic map (Krantz 1999, p. 16). The word derives from ...

All elementary functions can be extended to the complex plane. Such definitions agree with the real definitions on the x-axis and constitute an analytic continuation.

Complex Analysis

If a complex function f is analytic in a disk contained in a simply connected domain D and f can be analytically continued along every polygonal arc in D, then f can be ...

A function element is an ordered pair (f,U) where U is a disk D(Z_0,r) and f is an analytic function defined on U. If W is an open set, then a function element in W is a pair ...

A definable set which is the complement of an analytic set.