Continuous group action (original) (raw)
Uma ação contínua (AO 1945: acção), em topologia, de um grupo G num espaço topológico X é um homomorfismo de G no grupo dos homeomorfismos de X tal que a correspondente função é contínua.
| Property | Value |
|---|---|
| dbo:abstract | In topology, a continuous group action on a topological space X is a group action of a topological group G that is continuous: i.e., is a continuous map. Together with the group action, X is called a G-space. If is a continuous group homomorphism of topological groups and if X is a G-space, then H can act on X by restriction: , making X a H-space. Often f is either an inclusion or a quotient map. In particular, any topological space may be thought of as a G-space via (and G would act trivially.) Two basic operations are that of taking the space of points fixed by a subgroup H and that of forming a quotient by H. We write for the set of all x in X such that . For example, if we write for the set of continuous maps from a G-space X to another G-space Y, then, with the action , consists of f such that ; i.e., f is an equivariant map. We write . Note, for example, for a G-space X and a closed subgroup H, . (en) Uma ação contínua (AO 1945: acção), em topologia, de um grupo G num espaço topológico X é um homomorfismo de G no grupo dos homeomorfismos de X tal que a correspondente função é contínua. (pt) |
| dbo:wikiPageExternalLink | http://www.math.uchicago.edu/~may/PAPERS/Newthird.pdf |
| dbo:wikiPageID | 7522685 (xsd:integer) |
| dbo:wikiPageLength | 1917 (xsd:nonNegativeInteger) |
| dbo:wikiPageRevisionID | 1117528624 (xsd:integer) |
| dbo:wikiPageWikiLink | dbr:Lie_group_action dbr:Equivariant_map dbc:Topological_groups dbr:Topological_group dbr:Topology dbr:Group_action_(mathematics) dbc:Group_actions_(mathematics) dbr:Topological_space |
| dbp:wikiPageUsesTemplate | dbt:Cite_book dbt:Topology-stub |
| dct:subject | dbc:Topological_groups dbc:Group_actions_(mathematics) |
| rdf:type | yago:WikicatTopologicalGroups yago:Abstraction100002137 yago:Act100030358 yago:Event100029378 yago:Group100031264 yago:GroupAction101080366 yago:PsychologicalFeature100023100 yago:WikicatGroupActions yago:YagoPermanentlyLocatedEntity |
| rdfs:comment | Uma ação contínua (AO 1945: acção), em topologia, de um grupo G num espaço topológico X é um homomorfismo de G no grupo dos homeomorfismos de X tal que a correspondente função é contínua. (pt) In topology, a continuous group action on a topological space X is a group action of a topological group G that is continuous: i.e., is a continuous map. Together with the group action, X is called a G-space. If is a continuous group homomorphism of topological groups and if X is a G-space, then H can act on X by restriction: , making X a H-space. Often f is either an inclusion or a quotient map. In particular, any topological space may be thought of as a G-space via (and G would act trivially.) (en) |
| rdfs:label | Continuous group action (en) Ação de grupo contínua (pt) |
| owl:sameAs | freebase:Continuous group action yago-res:Continuous group action wikidata:Continuous group action dbpedia-pt:Continuous group action https://global.dbpedia.org/id/fv6g |
| prov:wasDerivedFrom | wikipedia-en:Continuous_group_action?oldid=1117528624&ns=0 |
| foaf:isPrimaryTopicOf | wikipedia-en:Continuous_group_action |
| is dbo:wikiPageDisambiguates of | dbr:Action |
| is dbo:wikiPageWikiLink of | dbr:Lie_group_action dbr:Glossary_of_algebraic_topology dbr:Topological_group dbr:Group_action dbr:Action dbr:Fiber_bundle_construction_theorem dbr:Structural_Ramsey_theory |
| is foaf:primaryTopic of | wikipedia-en:Continuous_group_action |