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Statements

Subject Item

dbr:Continuous_group_action

rdf:type

yago:Event100029378 yago:PsychologicalFeature100023100 yago:YagoPermanentlyLocatedEntity yago:GroupAction101080366 yago:Group100031264 yago:WikicatTopologicalGroups yago:Abstraction100002137 yago:WikicatGroupActions yago:Act100030358

rdfs:label

Ação de grupo contínua Continuous group action

rdfs:comment

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.) 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.

dcterms:subject

dbc:Topological_groups dbc:Group_actions_(mathematics)

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7522685

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1117528624

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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. 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, .

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wikipedia-en:Continuous_group_action?oldid=1117528624&ns=0

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1917

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wikipedia-en:Continuous_group_action