Faster access than browser!Similarities between 3-sphere and Hopf fibration
3-sphere and Hopf fibration have 24 things in common (in Unionpedia): Alexandroff extension, Circle, Circle bundle, Circle group, Complex number, Euclidean space, Fiber bundle, Four-dimensional space, Group action, Homeomorphism, Homotopy group, Homotopy groups of spheres, Hypersphere, N-sphere, Octonion, Quaternion, Quotient space (topology), Riemann sphere, Rotation group SO(3), Special unitary group, Sphere, Stereographic projection, Torus, Versor.
Alexandroff extension
In the mathematical field of topology, the Alexandroff extension is a way to extend a noncompact topological space by adjoining a single point in such a way that the resulting space is compact.
3-sphere and Alexandroff extension · Alexandroff extension and Hopf fibration ·
Circle
A circle is a simple closed shape.
3-sphere and Circle · Circle and Hopf fibration ·
Circle bundle
In mathematics, a circle bundle is a fiber bundle where the fiber is the circle \scriptstyle \mathbf^1.
3-sphere and Circle bundle · Circle bundle and Hopf fibration ·
Circle group
In mathematics, the circle group, denoted by T, is the multiplicative group of all complex numbers with absolute value 1, that is, the unit circle in the complex plane or simply the unit complex numbers The circle group forms a subgroup of C×, the multiplicative group of all nonzero complex numbers.
3-sphere and Circle group · Circle group and Hopf fibration ·
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.
3-sphere and Complex number · Complex number and Hopf fibration ·
Euclidean space
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
3-sphere and Euclidean space · Euclidean space and Hopf fibration ·
Fiber bundle
In mathematics, and particularly topology, a fiber bundle (or, in British English, fibre bundle) is a space that is locally a product space, but globally may have a different topological structure.
3-sphere and Fiber bundle · Fiber bundle and Hopf fibration ·
Four-dimensional space
A four-dimensional space or 4D space is a mathematical extension of the concept of three-dimensional or 3D space.
3-sphere and Four-dimensional space · Four-dimensional space and Hopf fibration ·
Group action
In mathematics, an action of a group is a formal way of interpreting the manner in which the elements of the group correspond to transformations of some space in a way that preserves the structure of that space.
3-sphere and Group action · Group action and Hopf fibration ·
Homeomorphism
In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function.
3-sphere and Homeomorphism · Homeomorphism and Hopf fibration ·
Homotopy group
In mathematics, homotopy groups are used in algebraic topology to classify topological spaces.
3-sphere and Homotopy group · Homotopy group and Hopf fibration ·
Homotopy groups of spheres
In the mathematical field of algebraic topology, the homotopy groups of spheres describe how spheres of various dimensions can wrap around each other.
3-sphere and Homotopy groups of spheres · Homotopy groups of spheres and Hopf fibration ·
Hypersphere
In geometry of higher dimensions, a hypersphere is the set of points at a constant distance from a given point called its center.
3-sphere and Hypersphere · Hopf fibration and Hypersphere ·
N-sphere
In mathematics, the n-sphere is the generalization of the ordinary sphere to spaces of arbitrary dimension.
3-sphere and N-sphere · Hopf fibration and N-sphere ·
Octonion
In mathematics, the octonions are a normed division algebra over the real numbers, usually represented by the capital letter O, using boldface O or blackboard bold \mathbb O. There are three lower-dimensional normed division algebras over the reals: the real numbers R themselves, the complex numbers C, and the quaternions H. The octonions have eight dimensions; twice the number of dimensions of the quaternions, of which they are an extension.
3-sphere and Octonion · Hopf fibration and Octonion ·
Quaternion
In mathematics, the quaternions are a number system that extends the complex numbers.
3-sphere and Quaternion · Hopf fibration and Quaternion ·
Quotient space (topology)
In topology and related areas of mathematics, a quotient space (also called an identification space) is, intuitively speaking, the result of identifying or "gluing together" certain points of a given topological space.
3-sphere and Quotient space (topology) · Hopf fibration and Quotient space (topology) ·
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.
3-sphere and Riemann sphere · Hopf fibration and Riemann sphere ·
Rotation group SO(3)
In mechanics and geometry, the 3D rotation group, often denoted SO(3), is the group of all rotations about the origin of three-dimensional Euclidean space R3 under the operation of composition.
3-sphere and Rotation group SO(3) · Hopf fibration and Rotation group SO(3) ·
Special unitary group
In mathematics, the special unitary group of degree, denoted, is the Lie group of unitary matrices with determinant 1.
3-sphere and Special unitary group · Hopf fibration and Special unitary group ·
Sphere
A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").
3-sphere and Sphere · Hopf fibration and Sphere ·
Stereographic projection
In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane.
3-sphere and Stereographic projection · Hopf fibration and Stereographic projection ·
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.
3-sphere and Torus · Hopf fibration and Torus ·
Versor
In mathematics, a versor is a quaternion of norm one (a unit quaternion).
The list above answers the following questions
- What 3-sphere and Hopf fibration have in common
- What are the similarities between 3-sphere and Hopf fibration
3-sphere and Hopf fibration Comparison
3-sphere has 103 relations, while Hopf fibration has 83. As they have in common 24, the Jaccard index is 12.90% = 24 / (103 + 83).
References
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