An analytic space is a generalization of an analytic manifold that allows singularities. An analytic space is a space that is locally the same as an analytic...

In mathematics, a rigid analytic space is an analogue of a complex analytic space over a nonarchimedean field. Such spaces were introduced by John Tate...

complex analytic variety or complex analytic space is a generalization of a complex manifold that allows the presence of singularities. Complex analytic varieties...

with complex manifolds and the more general analytic spaces defined locally by the vanishing of analytic functions of several complex variables. The deep...

In mathematics, a Berkovich space, introduced by Berkovich (1990), is a version of an analytic space over a non-Archimedean field (e.g. p-adic field),...

corresponding analytic space is a variety, but the algebraic space is not. Algebraic spaces over the complex numbers are closely related to analytic spaces and...

particular, it is a Stein manifold. Analytic space Complex coordinate space Complex polytope Exotic affine space *Berger, Marcel (1987), Geometry I, Berlin:...

an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions...

complex analytic space, or scheme. This perspective of equipping a topological space with a sheaf is essential to the theory of locally ringed spaces (see...

properties of these functions is called several complex variables (and analytic space), which the Mathematics Subject Classification has as a top-level heading...

theory, a subset of a Polish space X {\displaystyle X} is an analytic set if it is a continuous image of a Polish space. These sets were first defined...

contrasts with synthetic geometry. Analytic geometry is used in physics and engineering, and also in aviation, rocketry, space science, and spaceflight. It...

coherent. Likewise, if Z {\displaystyle Z} is a closed analytic subspace of a complex analytic space X {\displaystyle X} , the ideal sheaf I Z / X {\displaystyle...

real analytic manifolds, although complex manifolds are also analytic. In algebraic geometry, analytic spaces are a generalization of analytic manifolds...

Community A-Space, or Analytic Space, is a project started in 2007 from the Office of the Director of National Intelligence's (ODNI) Office of Analytic Transformation...

Taylor series (is analytic). Holomorphic functions are the central objects of study in complex analysis. Though the term analytic function is often used...

Look up analytic, analytical, or analyticity in Wiktionary, the free dictionary. Analytic or analytical may refer to: Analytical chemistry, the analysis...

generally coherent analytic sheaves) on X coincide with that of algebraic vector bundles. Chow's theorem says that a subset of projective space is the zero-locus...

holomorphic functions on a complex manifold or complex-analytic space. A complex manifold or complex space X {\displaystyle X} is said to be holomorphically...

Roughly speaking, γ(K) measures the size of the unit ball of the space of bounded analytic functions outside K. It was first introduced by Lars Ahlfors in...

morphism between schemes is an analog of a proper map between complex analytic spaces. Some authors call a proper variety over a field k {\displaystyle k}...

example, Tate's invention of rigid analytic spaces can be said to have spawned the entire field of rigid analytic geometry. He found a p-adic analogue...

Complex analytic space Drinfeld's symmetric space Eilenberg–Mac Lane space Euclidean space Fiber space Finsler space First-countable space Fréchet space Function...

The analytic–synthetic distinction is a semantic distinction used primarily in philosophy to distinguish between propositions (in particular, statements...

coherent analytic sheaf on a complex analytic space, and an analogous notion of a coherent algebraic sheaf on a scheme. In both cases, the given space X {\displaystyle...

notion can be defined on an arbitrary complex manifold or even a complex analytic space X {\displaystyle X} as follows. An upper semi-continuous function f...

f : X → S {\displaystyle f:X\to S} of complex-analytic spaces, schemes, or germs of functions on a space. Grothendieck was the first to find this far-reaching...

non-separable K-analytic spaces. Also, every Polish, Souslin, and reflexive Fréchet space is K-analytic as is the weak dual of a Frechet space. The generalized...

result of this, one can readily study singular spaces in complex geometry, such as singular complex analytic varieties or singular complex algebraic varieties...

complex analytic varieties are manifolds. Over a non-archimedean field analytic geometry is studied via rigid analytic spaces. Modern analytic geometry...