In mathematics, an n-dimensional differential structure (or differentiable structure) on a set M makes M into an n-dimensional differential manifold, which is a topological manifold with some additional structure that allows for differential calculus on the manifold. If M is already a topological manifold, it is required that the new topology be identical to the existing one.
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mathematics, an n-dimensional differentialstructure (or differentiable structure) on a set M makes M into an n-dimensional differential manifold, which is a topological...
manifold with a globally defined differentialstructure. Any topological manifold can be given a differentialstructure locally by using the homeomorphisms...
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It...
comparison differential topology is concerned with coarser properties, such as the number of holes in a manifold, its homotopy type, or the structure of its...
structures; and diffeomorphisms, which preserve differentialstructures. In 1939, the French group with the pseudonym Nicolas Bourbaki saw structures...
the natural differentialstructure of R n {\displaystyle \mathbb {R} ^{n}} (that is, if they are diffeomorphisms), the differentialstructure transfers...
spaces. A diffeomorphism is an isomorphism of spaces equipped with a differentialstructure, typically differentiable manifolds. A symplectomorphism is an isomorphism...
by adding structure to a topological manifold (e.g. differentiable manifolds are topological manifolds equipped with a differentialstructure). Every manifold...
the differentialstructure of smooth manifolds via de Rham cohomology, or Čech or sheaf cohomology to investigate the solvability of differential equations...
geometry or noncommutative geometry a quantum differential calculus or noncommutative differentialstructure on an algebra A {\displaystyle A} over a field...
systems of partial differential equations are usefully formulated, from the point of view of their underlying geometric and algebraic structure, in terms of...
This is a list of differential geometry topics. See also glossary of differential and metric geometry and list of Lie group topics. List of curves topics...
In mathematics, differential forms provide a unified approach to define integrands over curves, surfaces, solids, and higher-dimensional manifolds. The...
around its edges. The sedimentary rocks composing this structure dip outward at 10–20°. Differential erosion of resistant layers of quartzite has created...
In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with other...
In mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function...
mathematics, differential algebra is, broadly speaking, the area of mathematics consisting in the study of differential equations and differential operators...
the image subset S {\displaystyle S} together with a topology and differentialstructure such that S {\displaystyle S} is a manifold and the inclusion f...
methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs)....
(db)} . A differential graded algebra, DG-algebra or DGAlgebra is a graded algebra that is a differential graded module whose differential obeys the graded...
In mathematics, a differential operator is an operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first...
to the one-point compactification X* of X. Although we lose the differentialstructure of the original system we can now use compactness arguments to analyze...
In an area of mathematics called differential topology, an exotic sphere is a differentiable manifold M that is homeomorphic but not diffeomorphic to the...
differential graded algebra is a graded associative algebra with an added chain complex structure that respects the algebra structure. A differential...
In mathematics, a complex differential form is a differential form on a manifold (usually a complex manifold) which is permitted to have complex coefficients...
In differential geometry, a spin structure on an orientable Riemannian manifold (M, g) allows one to define associated spinor bundles, giving rise to...
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