# differential topology

differential topology
the branch of topology that studies the properties of differentiable manifolds that remain invariant under diffeomorphisms.

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Universalium. 2010.

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• Differential topology — In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. It is closely related to differential geometry and together they make up the geometric theory of differentiable manifolds.… …   Wikipedia

• differential topology — Math. the branch of topology that studies the properties of differentiable manifolds that remain invariant under diffeomorphisms …   Useful english dictionary

• differential topology — noun Field dealing with differentiable functions on differentiable manifolds …   Wiktionary

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• Rank (differential topology) — In mathematics, the rank of a differentiable map f : M → N between differentiable manifolds at a point p ∈ M is the rank of the derivative of f at p. Recall that the derivative of f at p is a linear map from the tangent space at p to the… …   Wikipedia

• Differential — may refer to: Contents 1 Mathematics 2 Natural sciences and engineering 3 Social sciences 4 Medicine 5 …   Wikipedia

• Topology — (Greek topos , place, and logos , study ) is the branch of mathematics that studies the properties of a space that are preserved under continuous deformations. Topology grew out of geometry, but unlike geometry, topology is not concerned with… …   Wikipedia

• Differential geometry — A triangle immersed in a saddle shape plane (a hyperbolic paraboloid), as well as two diverging ultraparallel lines. Differential geometry is a mathematical discipline that uses the techniques of differential and integral calculus, as well as… …   Wikipedia

• topology — topologic /top euh loj ik/, topological, adj. topologically, adv. topologist, n. /teuh pol euh jee/, n., pl. topologies for 3. Math. 1. the study of those properties of geometric forms that remain invariant under c …   Universalium

• Differential structure — 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 us to do differential …   Wikipedia