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44 relations: Antiderivative (complex analysis), Aquarium, Banach space, Cauchy's integral theorem, Complex analysis, Complex number, Conformal map, Connected space, Contractible space, Convex set, Covering space, Cylinder, Euclidean space, Fundamental group, Genus (mathematics), Handle decomposition, Hilbert space, Holomorphic function, Homotopy, Identity element, Klein bottle, Line integral, Long line (topology), Manifold, Möbius strip, Morphism, N-connected space, N-sphere, Orthogonal group, Poincaré conjecture, Projective plane, Retract, Riemann mapping theorem, Riemann sphere, Special unitary group, Theoretical physics, Topological space, Topological vector space, Topology, Torus, Unicoherent space, Unit circle, Unit disk, Wormhole.
Antiderivative (complex analysis)
In complex analysis, a branch of mathematics, the antiderivative, or primitive, of a complex-valued function g is a function whose complex derivative is g. More precisely, given an open set U in the complex plane and a function g:U\to \mathbb C, the antiderivative of g is a function f:U\to \mathbb C that satisfies \frac.
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Aquarium
An aquarium (plural: aquariums or aquaria) is a vivarium of any size having at least one transparent side in which aquatic plants or animals are kept and displayed.
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Banach space
In mathematics, more specifically in functional analysis, a Banach space (pronounced) is a complete normed vector space.
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Cauchy's integral theorem
In mathematics, the Cauchy integral theorem (also known as the Cauchy–Goursat theorem) in complex analysis, named after Augustin-Louis Cauchy (and Édouard Goursat), is an important statement about line integrals for holomorphic functions in the complex plane.
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Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.
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Complex number
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
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Conformal map
In mathematics, a conformal map is a function that preserves angles locally.
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Connected space
In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint nonempty open subsets.
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Contractible space
In mathematics, a topological space X is contractible if the identity map on X is null-homotopic, i.e. if it is homotopic to some constant map.
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Convex set
In convex geometry, a convex set is a subset of an affine space that is closed under convex combinations.
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Covering space
In mathematics, more specifically algebraic topology, a covering map (also covering projection) is a continuous function p from a topological space, C, to a topological space, X, such that each point in X has an open neighbourhood evenly covered by p (as shown in the image); the precise definition is given below.
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Cylinder
A cylinder (from Greek κύλινδρος – kulindros, "roller, tumbler"), has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes.
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Euclidean space
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
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Fundamental group
In the mathematical field of algebraic topology, the fundamental group is a mathematical group associated to any given pointed topological space that provides a way to determine when two paths, starting and ending at a fixed base point, can be continuously deformed into each other.
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Genus (mathematics)
In mathematics, genus (plural genera) has a few different, but closely related, meanings.
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Handle decomposition
In mathematics, a handle decomposition of an m-manifold M is a union where each M_i is obtained from M_ by the attaching of i-handles.
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Hilbert space
The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space.
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Holomorphic function
In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighborhood of every point in its domain.
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Homotopy
In topology, two continuous functions from one topological space to another are called homotopic (from Greek ὁμός homós "same, similar" and τόπος tópos "place") if one can be "continuously deformed" into the other, such a deformation being called a homotopy between the two functions.
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Identity element
In mathematics, an identity element or neutral element is a special type of element of a set with respect to a binary operation on that set, which leaves other elements unchanged when combined with them.
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Klein bottle
In topology, a branch of mathematics, the Klein bottle is an example of a non-orientable surface; it is a two-dimensional manifold against which a system for determining a normal vector cannot be consistently defined.
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Line integral
In mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve.
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Long line (topology)
In topology, the long line (or Alexandroff line) is a topological space somewhat similar to the real line, but in a certain way "longer".
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Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.
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Möbius strip
The Möbius strip or Möbius band, also spelled Mobius or Moebius, is a surface with only one side (when embedded in three-dimensional Euclidean space) and only one boundary.
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Morphism
In mathematics, a morphism is a structure-preserving map from one mathematical structure to another one of the same type.
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N-connected space
In the mathematical branch of algebraic topology, specifically homotopy theory, n-connectedness (sometimes, n-simple connectedness) generalizes the concepts of path-connectedness and simple connectedness.
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N-sphere
In mathematics, the n-sphere is the generalization of the ordinary sphere to spaces of arbitrary dimension.
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Orthogonal group
In mathematics, the orthogonal group in dimension, denoted, is the group of distance-preserving transformations of a Euclidean space of dimension that preserve a fixed point, where the group operation is given by composing transformations.
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Poincaré conjecture
In mathematics, the Poincaré conjecture is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space.
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Projective plane
In mathematics, a projective plane is a geometric structure that extends the concept of a plane.
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Retract
In topology, a branch of mathematics, a retraction is a continuous mapping from a topological space into a subspace which preserves the position of all points in that subspace.
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Riemann mapping theorem
In complex analysis, the Riemann mapping theorem states that if U is a non-empty simply connected open subset of the complex number plane C which is not all of C, then there exists a biholomorphic mapping f (i.e. a bijective holomorphic mapping whose inverse is also holomorphic) from U onto the open unit disk This mapping is known as a Riemann mapping.
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Riemann sphere
In mathematics, the Riemann sphere, named after Bernhard Riemann, is a model of the extended complex plane, the complex plane plus a point at infinity.
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Special unitary group
In mathematics, the special unitary group of degree, denoted, is the Lie group of unitary matrices with determinant 1.
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Theoretical physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena.
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Topological space
In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods.
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Topological vector space
In mathematics, a topological vector space (also called a linear topological space) is one of the basic structures investigated in functional analysis.
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Topology
In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.
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Torus
In geometry, a torus (plural tori) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle.
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Unicoherent space
In mathematics, a unicoherent space is a topological space X that is connected and in which the following property holds: For any closed, connected A, B \subset X with X.
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Unit circle
In mathematics, a unit circle is a circle with a radius of one.
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Unit disk
In mathematics, the open unit disk (or disc) around P (where P is a given point in the plane), is the set of points whose distance from P is less than 1: The closed unit disk around P is the set of points whose distance from P is less than or equal to one: Unit disks are special cases of disks and unit balls; as such, they contain the interior of the unit circle and, in the case of the closed unit disk, the unit circle itself.
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Wormhole
A wormhole is a concept that represents a solution of the Einstein field equations: a non-trivial resolution of the Ehrenfest paradox structure linking separate points in spacetime.
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1-Connected, 1-connected, Doubly connected, Multiply connected, Multiply-connected, Non-simply-connected, Simply Connected, Simply connected, Simply connected domain, Simply connected set, Simply-connected, Simply-connected domain, Simply-connected set, Singly connected.
References
[1] https://en.wikipedia.org/wiki/Simply_connected_space
