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.
Circle and Fiber bundle · Circle and Torus ·
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.
Cohomology and Fiber bundle · Cohomology and Torus ·
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 ·
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.
Connected space and Fiber bundle · Connected space and Torus ·
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.
Exact sequence and Fiber bundle · Exact sequence 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.
Fiber bundle and Group action · 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.
Fiber bundle and Homeomorphism · 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.
Fiber bundle and Homotopy · Homotopy and Torus ·
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.
Fiber bundle and Hopf fibration · Hopf fibration and Torus ·
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.
Fiber bundle and Klein bottle · Klein bottle and Torus ·
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.
Fiber bundle and Lie group · Lie group and Torus ·
Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.
Fiber bundle and Manifold · Manifold and Torus ·
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 ·
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.
Fiber bundle and Möbius strip · Möbius strip 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.
Fiber bundle 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.
Fiber bundle and Quotient space (topology) · Quotient space (topology) and Torus ·
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.
Fiber bundle and Riemannian manifold · Riemannian manifold and Torus ·
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 ·
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.
The list above answers the following questions
- What Fiber bundle and Torus have in common
- What are the similarities between Fiber bundle and Torus
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
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