Information om | Engelska ordet N-SPHERE

Exempel på hur man kan använda N-SPHERE i en mening

• In mathematics, the Borsuk–Ulam theorem states that every continuous function from an n-sphere into Euclidean n-space maps some pair of antipodal points to the same point.
• The n-sphere is a locally conformally flat manifold that is not globally conformally flat in this sense, whereas a Euclidean space, a torus, or any conformal manifold that is covered by an open subset of Euclidean space is (globally) conformally flat in this sense.
• In mathematics, two points of a sphere (or n-sphere, including a circle) are called antipodal or diametrically opposite if they are the endpoints of a diameter, a straight line segment between two points on a sphere and passing through its center.
• Antipodal point, the diametrically opposite point on a circle or n-sphere, also known as an antipode.
• In an area of mathematics called differential topology, an exotic sphere is a differentiable manifold M that is homeomorphic but not diffeomorphic to the standard Euclidean n-sphere.
• The topological generalized Poincaré conjecture is that any n-dimensional homotopy sphere is homeomorphic to the n-sphere; it was solved by Stephen Smale in dimensions five and higher, by Michael Freedman in dimension 4, and for dimension 3 (the original Poincaré conjecture) by Grigori Perelman in 2005.
• Exotic sphere, a differentiable n-manifold, homeomorphic but not diffeomorphic to the ordinary n-sphere.
• The arc, the n-sphere, and the Hilbert cube are examples of path-connected continua; the topologist's sine curve is an example of a continuum that is not path-connected.
• Shortly after Smale's announcement of a proof, John Stallings gave a different proof for dimensions at least 7 that a PL homotopy n-sphere was homeomorphic to the n-sphere, using the notion of "engulfing".
• The development of a conformally flat manifold is a conformal local diffeomorphism from the universal cover of the manifold to the n-sphere.

Förberedelsen av sidan tog: 496,53 ms.