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  2. Restricted root system - Wikipedia

    en.wikipedia.org/wiki/Restricted_root_system

    The restricted root system of a symmetric space and its dual can be identified. For symmetric spaces of noncompact type arising as homogeneous spaces of a semisimple Lie group , the restricted root system and its Weyl group are related to the Iwasawa decomposition of the Lie group.

  3. For example, on the International Space Station the Earth's gravity is nearly 90% as strong as at the surface. Objects orbiting in space would not remain in orbit if not for the gravitational force, and gravitational fields extend even into the depths of intergalactic space. [5] [6] [7] The dark side of the Moon illuminated by the Sun.

  4. Restriction (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Restriction_(mathematics)

    Let , be two closed subsets (or two open subsets) of a topological space such that =, and let also be a topological space. If f : A → B {\displaystyle f:A\to B} is continuous when restricted to both X {\displaystyle X} and Y , {\displaystyle Y,} then f {\displaystyle f} is continuous.

  5. Configuration space (physics) - Wikipedia

    en.wikipedia.org/wiki/Configuration_space_(physics)

    The set of coordinates that define the position of a reference point and the orientation of a coordinate frame attached to a rigid body in three-dimensional space form its configuration space, often denoted () where represents the coordinates of the origin of the frame attached to the body, and () represents the rotation matrices that define the orientation of this frame relative to a ground ...

  6. Space (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Space_(mathematics)

    A space consists of selected mathematical objects that are treated as points, and selected relationships between these points. The nature of the points can vary widely: for example, the points can represent numbers, functions on another space, or subspaces of another space. It is the relationships that define the nature of the space.

  7. Kissing number - Wikipedia

    en.wikipedia.org/wiki/Kissing_number

    In three dimensions, the kissing number is 12, but the correct value was much more difficult to establish than in dimensions one and two. It is easy to arrange 12 spheres so that each touches a central sphere, with a lot of space left over, and it is not obvious that there is no way to pack in a 13th sphere.

  8. Projection (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Projection_(mathematics)

    The concept of projection in mathematics is a very old one, and most likely has its roots in the phenomenon of the shadows cast by real-world objects on the ground. This rudimentary idea was refined and abstracted, first in a geometric context and later in other branches of mathematics. Over time different versions of the concept developed, but ...

  9. Moduli space - Wikipedia

    en.wikipedia.org/wiki/Moduli_space

    A space M is a fine moduli space for the functor F if M represents F, i.e., there is a natural isomorphism τ : F → Hom(−, M), where Hom(−, M) is the functor of points. This implies that M carries a universal family; this family is the family on M corresponding to the identity map 1 M ∊ Hom(M, M).

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