Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Discrete_group> ?p ?o }
- Discrete_group abstract "In mathematics, a discrete group is a group G equipped with the discrete topology. With this topology, G becomes a topological group. A discrete subgroup of a topological group G is a subgroup H whose relative topology is the discrete one. For example, the integers, Z, form a discrete subgroup of the reals, R (with the standard metric topology), but the rational numbers, Q, do not.Any group can be given the discrete topology. Since every map from a discrete space is continuous, the topological homomorphisms between discrete groups are exactly the group homomorphisms between the underlying groups. Hence, there is an isomorphism between the category of groups and the category of discrete groups. Discrete groups can therefore be identified with their underlying (non-topological) groups.There are some occasions when a topological group or Lie group is usefully endowed with the discrete topology, 'against nature'. This happens for example in the theory of the Bohr compactification, and in group cohomology theory of Lie groups.A discrete isometry group is an isometry group such that for every point of the metric space the set of images of the point under the isometries is a discrete set. A discrete symmetry group is a symmetry group that is a discrete isometry group.".
- Discrete_group thumbnail Number-line.svg?width=300.
- Discrete_group wikiPageID "468536".
- Discrete_group wikiPageLength "6091".
- Discrete_group wikiPageOutDegree "72".
- Discrete_group wikiPageRevisionID "668598567".
- Discrete_group wikiPageWikiLink Abelian_group.
- Discrete_group wikiPageWikiLink Arithmetic_group.
- Discrete_group wikiPageWikiLink Bohr_compactification.
- Discrete_group wikiPageWikiLink Category:Discrete_groups.
- Discrete_group wikiPageWikiLink Category:Geometric_group_theory.
- Discrete_group wikiPageWikiLink Category_of_groups.
- Discrete_group wikiPageWikiLink Center_(group_theory).
- Discrete_group wikiPageWikiLink Compact_group.
- Discrete_group wikiPageWikiLink Compact_space.
- Discrete_group wikiPageWikiLink Compact_subset.
- Discrete_group wikiPageWikiLink Computational_group_theory.
- Discrete_group wikiPageWikiLink Congruence_subgroup.
- Discrete_group wikiPageWikiLink Connected_space.
- Discrete_group wikiPageWikiLink Continuous_(topology).
- Discrete_group wikiPageWikiLink Continuous_function.
- Discrete_group wikiPageWikiLink Covering_group.
- Discrete_group wikiPageWikiLink Crystallographic_group.
- Discrete_group wikiPageWikiLink Crystallographic_point_group.
- Discrete_group wikiPageWikiLink Discrete_set.
- Discrete_group wikiPageWikiLink Discrete_space.
- Discrete_group wikiPageWikiLink Discrete_topology.
- Discrete_group wikiPageWikiLink Free_regular_set.
- Discrete_group wikiPageWikiLink Freely_discontinuous.
- Discrete_group wikiPageWikiLink Frieze_group.
- Discrete_group wikiPageWikiLink Fuchsian_group.
- Discrete_group wikiPageWikiLink Geometric_group_theory.
- Discrete_group wikiPageWikiLink Group_(mathematics).
- Discrete_group wikiPageWikiLink Group_cohomology.
- Discrete_group wikiPageWikiLink Group_homomorphism.
- Discrete_group wikiPageWikiLink Group_of_components.
- Discrete_group wikiPageWikiLink Haar_measure.
- Discrete_group wikiPageWikiLink Half-space_(geometry).
- Discrete_group wikiPageWikiLink Hausdorff_space.
- Discrete_group wikiPageWikiLink Hausdorff_topology.
- Discrete_group wikiPageWikiLink Homogeneous_space.
- Discrete_group wikiPageWikiLink Hyperbolic_3-space.
- Discrete_group wikiPageWikiLink Hyperbolic_space.
- Discrete_group wikiPageWikiLink Identity_component.
- Discrete_group wikiPageWikiLink Index_of_a_subgroup.
- Discrete_group wikiPageWikiLink Integer.
- Discrete_group wikiPageWikiLink Isolated_point.
- Discrete_group wikiPageWikiLink Isometry_group.
- Discrete_group wikiPageWikiLink Isomorphism_of_categories.
- Discrete_group wikiPageWikiLink Kleinian_group.
- Discrete_group wikiPageWikiLink Lattice_(discrete_subgroup).
- Discrete_group wikiPageWikiLink Lie_group.
- Discrete_group wikiPageWikiLink Locally_compact_group.
- Discrete_group wikiPageWikiLink Locally_isomorphic_groups.
- Discrete_group wikiPageWikiLink Mathematics.
- Discrete_group wikiPageWikiLink Metric_space.
- Discrete_group wikiPageWikiLink Modular_group.
- Discrete_group wikiPageWikiLink Normal_subgroup.
- Discrete_group wikiPageWikiLink Open_set.
- Discrete_group wikiPageWikiLink Quasi-Fuchsian_group.
- Discrete_group wikiPageWikiLink Quotient_group.
- Discrete_group wikiPageWikiLink Rational_number.
- Discrete_group wikiPageWikiLink Real_number.
- Discrete_group wikiPageWikiLink Real_numbers.
- Discrete_group wikiPageWikiLink Relative_topology.
- Discrete_group wikiPageWikiLink Second-countable.
- Discrete_group wikiPageWikiLink Second-countable_space.
- Discrete_group wikiPageWikiLink Singleton_(mathematics).
- Discrete_group wikiPageWikiLink Solvable_Lie_algebra.
- Discrete_group wikiPageWikiLink Solvable_Lie_group.
- Discrete_group wikiPageWikiLink Space_group.
- Discrete_group wikiPageWikiLink Subgroup.
- Discrete_group wikiPageWikiLink Subspace_topology.
- Discrete_group wikiPageWikiLink Symmetry_group.
- Discrete_group wikiPageWikiLink Topological_group.
- Discrete_group wikiPageWikiLink Totally_disconnected.
- Discrete_group wikiPageWikiLink Totally_disconnected_space.
- Discrete_group wikiPageWikiLink Triangle_group.
- Discrete_group wikiPageWikiLink Trivial_group.
- Discrete_group wikiPageWikiLink Uncountable.
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- Discrete_group wikiPageWikiLink Upper_half-plane.
- Discrete_group wikiPageWikiLink Upper_half-space.
- Discrete_group wikiPageWikiLink Wallpaper_group.
- Discrete_group wikiPageWikiLink File:Number-line.svg.
- Discrete_group wikiPageWikiLinkText "Discrete group".
- Discrete_group wikiPageWikiLinkText "discrete group".
- Discrete_group wikiPageWikiLinkText "discrete subgroup".
- Discrete_group wikiPageWikiLinkText "discrete subgroups".
- Discrete_group wikiPageWikiLinkText "discrete".
- Discrete_group wikiPageWikiLinkText "discretely".
- Discrete_group wikiPageWikiLinkText "discreteness".
- Discrete_group hasPhotoCollection Discrete_group.
- Discrete_group id "d/d033080".
- Discrete_group id "d/d033150".
- Discrete_group title "Discrete group of transformations".
- Discrete_group title "Discrete subgroup".
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- Discrete_group wikiPageUsesTemplate Template:Springer.
- Discrete_group wikiPageUsesTemplate Template:Technical.