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- 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.".
- Discrete_group thumbnail Number-line.svg?width=300.
- Discrete_group wikiPageID "468536".
- Discrete_group wikiPageRevisionID "605626770".
- 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".
- Discrete_group subject Category:Discrete_groups.
- Discrete_group subject Category:Geometric_group_theory.
- Discrete_group type Abstraction100002137.
- Discrete_group type DiscreteGroups.
- Discrete_group type Group100031264.
- Discrete_group comment "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.".
- Discrete_group label "Discrete groep".
- Discrete_group label "Discrete group".
- Discrete_group label "Diskrete Untergruppe".
- Discrete_group label "Groupe discret".
- Discrete_group label "Grupa dyskretna".
- Discrete_group label "Grupo discreto".
- Discrete_group label "離散群".
- Discrete_group sameAs Diskrete_Untergruppe.
- Discrete_group sameAs Grupo_discreto.
- Discrete_group sameAs Groupe_discret.
- Discrete_group sameAs 이산_군.
- Discrete_group sameAs Discrete_groep.
- Discrete_group sameAs Grupa_dyskretna.
- Discrete_group sameAs m.02d4qy.
- Discrete_group sameAs Q1361055.
- Discrete_group sameAs Q1361055.
- Discrete_group sameAs Discrete_group.
- Discrete_group wasDerivedFrom Discrete_group?oldid=605626770.
- Discrete_group depiction Number-line.svg.
- Discrete_group isPrimaryTopicOf Discrete_group.
