Faster access than browser!Similarities between Hopf fibration and Torus
Hopf fibration and Torus have 19 things in common (in Unionpedia): Cartesian coordinate system, Circle, Complex coordinate space, Complex number, Diffeomorphism, Embedding, Euclidean space, Fiber bundle, Four-dimensional space, Group action, Homeomorphism, Homotopy, Isometry, Product topology, Quotient space (topology), Sphere, Stereographic projection, Villarceau circles, 3-sphere.
Cartesian coordinate system
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.
Cartesian coordinate system and Hopf fibration · Cartesian coordinate system and Torus ·
Circle
A circle is a simple closed shape.
Circle and Hopf fibration · Circle and Torus ·
Complex coordinate space
In mathematics, the n-dimensional complex coordinate space (or complex n-space) is the set of all ordered n-tuples of complex numbers.
Complex coordinate space and Hopf fibration · Complex coordinate space and Torus ·
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.
Complex number and Hopf fibration · Complex number and Torus ·
Diffeomorphism
In mathematics, a diffeomorphism is an isomorphism of smooth manifolds.
Diffeomorphism and Hopf fibration · Diffeomorphism and Torus ·
Embedding
In mathematics, an embedding (or imbedding) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup.
Embedding and Hopf fibration · Embedding and Torus ·
Euclidean space
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
Euclidean space and Hopf fibration · Euclidean space and Torus ·
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.
Fiber bundle and Hopf fibration · Fiber bundle and Torus ·
Four-dimensional space
A four-dimensional space or 4D space is a mathematical extension of the concept of three-dimensional or 3D space.
Four-dimensional space and Hopf fibration · Four-dimensional space and Torus ·
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.
Group action and Hopf fibration · Group action and Torus ·
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.
Homeomorphism and Hopf fibration · Homeomorphism and Torus ·
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.
Homotopy and Hopf fibration · Homotopy and Torus ·
Isometry
In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective.
Hopf fibration and Isometry · Isometry and Torus ·
Product topology
In topology and related areas of mathematics, a product space is the cartesian product of a family of topological spaces equipped with a natural topology called the product topology.
Hopf fibration and Product topology · Product topology and Torus ·
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.
Hopf fibration and Quotient space (topology) · Quotient space (topology) and Torus ·
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").
Hopf fibration and Sphere · Sphere and Torus ·
Stereographic projection
In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane.
Hopf fibration and Stereographic projection · Stereographic projection and Torus ·
Villarceau circles
In geometry, Villarceau circles are a pair of circles produced by cutting a torus obliquely through the center at a special angle.
Hopf fibration and Villarceau circles · Torus and Villarceau circles ·
3-sphere
In mathematics, a 3-sphere, or glome, is a higher-dimensional analogue of a sphere.
The list above answers the following questions
- What Hopf fibration and Torus have in common
- What are the similarities between Hopf fibration and Torus
Hopf fibration and Torus Comparison
Hopf fibration has 83 relations, while Torus has 146. As they have in common 19, the Jaccard index is 8.30% = 19 / (83 + 146).
References
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