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- Homogeneous_space abstract "In mathematics, particularly in the theories of Lie groups, algebraic groups and topological groups, a homogeneous space for a group G is a non-empty manifold or topological space X on which G acts continuously and transitively. The elements of G are called the symmetries of X. A special case of this is when the group G in question is the automorphism group of the space X – here "automorphism group" can mean isometry group, diffeomorphism group, or homeomorphism group. In this case X is homogeneous if intuitively X looks locally the same at each point, either in the sense of isometry (rigid geometry), diffeomorphism (differential geometry), or homeomorphism (topology). Some authors insist that the action of G be faithful (non-identity elements act non-trivially), although the present article does not. Thus there is a group action of G on X which can be thought of as preserving some "geometric structure" on X, and making X into a single G-orbit.".
- Homogeneous_space wikiPageID "363325".
- Homogeneous_space wikiPageRevisionID "602277996".
- Homogeneous_space hasPhotoCollection Homogeneous_space.
- Homogeneous_space subject Category:Homogeneous_spaces.
- Homogeneous_space subject Category:Lie_groups.
- Homogeneous_space subject Category:Topological_groups.
- Homogeneous_space type Abstraction100002137.
- Homogeneous_space type Attribute100024264.
- Homogeneous_space type Group100031264.
- Homogeneous_space type HomogeneousSpaces.
- Homogeneous_space type LieGroups.
- Homogeneous_space type Space100028651.
- Homogeneous_space type TopologicalGroups.
- Homogeneous_space comment "In mathematics, particularly in the theories of Lie groups, algebraic groups and topological groups, a homogeneous space for a group G is a non-empty manifold or topological space X on which G acts continuously and transitively. The elements of G are called the symmetries of X. A special case of this is when the group G in question is the automorphism group of the space X – here "automorphism group" can mean isometry group, diffeomorphism group, or homeomorphism group.".
- Homogeneous_space label "Espace homogène".
- Homogeneous_space label "Homogene ruimte".
- Homogeneous_space label "Homogeneous space".
- Homogeneous_space label "Przestrzeń jednorodna".
- Homogeneous_space label "Spazio omogeneo".
- Homogeneous_space label "Однородное пространство".
- Homogeneous_space label "齐性空间".
- Homogeneous_space sameAs Espace_homogène.
- Homogeneous_space sameAs Spazio_omogeneo.
- Homogeneous_space sameAs 동차공간.
- Homogeneous_space sameAs Homogene_ruimte.
- Homogeneous_space sameAs Przestrzeń_jednorodna.
- Homogeneous_space sameAs m.01_pkc.
- Homogeneous_space sameAs Q1324364.
- Homogeneous_space sameAs Q1324364.
- Homogeneous_space sameAs Homogeneous_space.
- Homogeneous_space wasDerivedFrom Homogeneous_space?oldid=602277996.
- Homogeneous_space isPrimaryTopicOf Homogeneous_space.