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space periodicity - translation to russian
математика
пространственная периодичность
![A right-handed three-dimensional [[Cartesian coordinate system]] used to indicate positions in space<!--(See diagram description for needed correction.)-->](https://commons.wikimedia.org/wiki/Special:FilePath/3D coordinate system.svg?width=200 "A right-handed three-dimensional [[Cartesian coordinate system]] used to indicate positions in space<!--(See diagram description for needed correction.)-->")
![[[Cartesian coordinate system]]](https://commons.wikimedia.org/wiki/Special:FilePath/Coord XYZ.svg?width=200 "[[Cartesian coordinate system]]")
![[[Cylindrical coordinate system]]](https://commons.wikimedia.org/wiki/Special:FilePath/Cylindrical Coordinates.svg?width=200 "[[Cylindrical coordinate system]]")
![[[Spherical coordinate system]]](https://commons.wikimedia.org/wiki/Special:FilePath/Spherical Coordinates (Colatitude, Longitude).svg?width=200 "[[Spherical coordinate system]]")
математика
трехмерное пространство
- cipher space
- cipher text space
- code space
- cryptogram space
- cryptographlc space
- decision space
- interblock space
- key space
- linear space
- linear vector space
- message space
- observation space
- parameter space
- password space
- plaintext space
- probability space
- protected space
- sampie space
- search space
- security space
- solution space
- time-frequency space
- vector space
- vector space of dimension n
Definition
Wikipedia
In mathematics, the Bott periodicity theorem describes a periodicity in the homotopy groups of classical groups, discovered by Raoul Bott (1957, 1959), which proved to be of foundational significance for much further research, in particular in K-theory of stable complex vector bundles, as well as the stable homotopy groups of spheres. Bott periodicity can be formulated in numerous ways, with the periodicity in question always appearing as a period-2 phenomenon, with respect to dimension, for the theory associated to the unitary group. See for example topological K-theory.
There are corresponding period-8 phenomena for the matching theories, (real) KO-theory and (quaternionic) KSp-theory, associated to the real orthogonal group and the quaternionic symplectic group, respectively. The J-homomorphism is a homomorphism from the homotopy groups of orthogonal groups to stable homotopy groups of spheres, which causes the period 8 Bott periodicity to be visible in the stable homotopy groups of spheres.
