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Fiber bundle and Torus

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Fiber bundle and Torus

Fiber bundle vs. Torus

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. 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.

Similarities between Fiber bundle and Torus

Fiber bundle and Torus have 19 things in common (in Unionpedia): Circle, Cohomology, Compact space, Connected space, Exact sequence, Group action, Homeomorphism, Homotopy, Hopf fibration, Klein bottle, Lie group, Manifold, Map (mathematics), Möbius strip, Product topology, Quotient space (topology), Riemannian manifold, Smoothness, Topology.

Circle

A circle is a simple closed shape.

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Cohomology

In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups associated to a topological space, often defined from a cochain complex.

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Compact space

In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).

Compact space and Fiber bundle · Compact space and Torus · See more »

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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Exact sequence

An exact sequence is a concept in mathematics, especially in group theory, ring and module theory, homological algebra, as well as in differential geometry.

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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.

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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.

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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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Hopf fibration

In the mathematical field of differential topology, the Hopf fibration (also known as the Hopf bundle or Hopf map) describes a 3-sphere (a hypersphere in four-dimensional space) in terms of circles and an ordinary sphere.

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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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Lie group

In mathematics, a Lie group (pronounced "Lee") is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure.

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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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Map (mathematics)

In mathematics, the term mapping, sometimes shortened to map, refers to either a function, often with some sort of special structure, or a morphism in category theory, which generalizes the idea of a function.

Fiber bundle and Map (mathematics) · Map (mathematics) and Torus · See more »

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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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.

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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.

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Riemannian manifold

In differential geometry, a (smooth) Riemannian manifold or (smooth) Riemannian space (M,g) is a real, smooth manifold M equipped with an inner product g_p on the tangent space T_pM at each point p that varies smoothly from point to point in the sense that if X and Y are differentiable vector fields on M, then p \mapsto g_p(X(p),Y(p)) is a smooth function.

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Smoothness

In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.

Fiber bundle and Smoothness · Smoothness and Torus · See more »

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.

Fiber bundle and Topology · Topology and Torus · See more »

The list above answers the following questions

Fiber bundle and Torus Comparison

Fiber bundle has 110 relations, while Torus has 146. As they have in common 19, the Jaccard index is 7.42% = 19 / (110 + 146).

References

This article shows the relationship between Fiber bundle and Torus. To access each article from which the information was extracted, please visit:

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