About: Hilbert manifold

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In mathematics, a Hilbert manifold is a manifold modeled on Hilbert spaces. Thus it is a separable Hausdorff space in which each point has a neighbourhood homeomorphic to an infinite dimensional Hilbert space. The concept of a Hilbert manifold provides a possibility of extending the theory of manifolds to infinite-dimensional setting. Analogously to the finite-dimensional situation, one can define a differentiable Hilbert manifold by considering a maximal atlas in which the transition maps are differentiable.

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rdf:type	yago:WikicatManifolds yago:WikicatStructuresOnManifolds yago:Artifact100021939 yago:Conduit103089014 yago:Manifold103717750 yago:Object100002684 yago:Passage103895293 yago:PhysicalEntity100001930 yago:Pipe103944672 yago:YagoGeoEntity yago:YagoPermanentlyLocatedEntity yago:Structure104341686 yago:Tube104493505 yago:Way104564698 yago:Whole100003553
rdfs:label	Hilberta sternaĵo (eo) Hilbert manifold (en) Variété de Hilbert (fr) 힐베르트 다양체 (ko) Гильбертово многообразие (ru)
rdfs:comment	En matematiko, hilberta sternaĵo estas sternaĵo modelita en hilberta spaco. Tial ĝi estas topologia spaco en kiu ĉiu punkto havas najbarecon homeomorfan al hilberta spaco. Hilbertaj sternaĵoj estas unu el eblaj specoj de sternaĵoj en malfiniaj dimensioj. (eo) In mathematics, a Hilbert manifold is a manifold modeled on Hilbert spaces. Thus it is a separable Hausdorff space in which each point has a neighbourhood homeomorphic to an infinite dimensional Hilbert space. The concept of a Hilbert manifold provides a possibility of extending the theory of manifolds to infinite-dimensional setting. Analogously to the finite-dimensional situation, one can define a differentiable Hilbert manifold by considering a maximal atlas in which the transition maps are differentiable. (en) 기하학에서, 힐베르트 다양체(Hilbert多樣體, 영어: Hilbert manifold)는 국소적으로 힐베르트 공간과 동형인 위상 공간이다. (ko)
dcterms:subject	Differential geometry Structures on manifolds Riemannian manifolds Manifolds Generalized manifolds Nonlinear functional analysis Riemannian geometry General topology
Wikipage page ID	2504412 (xsd:integer)
Wikipage revision ID	1119698153 (xsd:integer)
Link from a Wikipage to another Wikipage	Homeomorphic Homotopy equivalence Differential geometry Structures on manifolds Compact space Critical point (mathematics) Mathematics Separable space Riemannian manifolds Submanifold Sobolev space Function space Kuiper's theorem Tangent space Tubular neighbourhood Hausdorff space Manifolds Exotic sphere Generalized manifolds Nonlinear functional analysis Diffeomorphism Lens space Riemannian manifold Hilbert space Riemannian geometry General topology Codimension Manifold CW complex Fredholm operator Identity function Open set Loop space Sard's lemma Vector bundle Hilbert spaces Parallelizable String topology Topological space Free loop space Compact open topology Homotopy type
Link from a Wikipage to an external page	http://www.map.mpim-bonn.mpg.de/Hilbert_manifold https://arxiv.org/abs/math.at/0306080
sameAs	Hilbert manifold Hilbert manifold Hilbert manifold Hilbert manifold Hilbert manifold Hilbert manifold Hilbert manifold Hilbert manifold
dbp:wikiPageUsesTemplate	dbt:Annotated_link dbt:Citation dbt:Reflist dbt:Riemannian_geometry dbt:Analysis_in_topological_vector_spaces dbt:Functional_analysis dbt:Hilbert_space dbt:Manifolds
has abstract	En matematiko, hilberta sternaĵo estas sternaĵo modelita en hilberta spaco. Tial ĝi estas topologia spaco en kiu ĉiu punkto havas najbarecon homeomorfan al hilberta spaco. Hilbertaj sternaĵoj estas unu el eblaj specoj de sternaĵoj en malfiniaj dimensioj. (eo) In mathematics, a Hilbert manifold is a manifold modeled on Hilbert spaces. Thus it is a separable Hausdorff space in which each point has a neighbourhood homeomorphic to an infinite dimensional Hilbert space. The concept of a Hilbert manifold provides a possibility of extending the theory of manifolds to infinite-dimensional setting. Analogously to the finite-dimensional situation, one can define a differentiable Hilbert manifold by considering a maximal atlas in which the transition maps are differentiable. (en) 기하학에서, 힐베르트 다양체(Hilbert多樣體, 영어: Hilbert manifold)는 국소적으로 힐베르트 공간과 동형인 위상 공간이다. (ko)
gold:hypernym	Manifold
prov:wasDerivedFrom	wikipedia-en:Hilbert_manifold?oldid=1119698153&ns=0
page length (characters) of wiki page	5880 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Hilbert_manifold

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