About: Banach manifold

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In mathematics, a Banach manifold is a manifold modeled on Banach spaces. Thus it is a topological space in which each point has a neighbourhood homeomorphic to an open set in a Banach space (a more involved and formal definition is given below). Banach manifolds are one possibility of extending manifolds to infinite dimensions. A further generalisation is to Fréchet manifolds, replacing Banach spaces by Fréchet spaces. On the other hand, a Hilbert manifold is a special case of a Banach manifold in which the manifold is locally modeled on Hilbert spaces.

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rdfs:label	Banach-Mannigfaltigkeit (de) Banach manifold (en) Variedad de Banach (es)
rdfs:comment	Eine Banach-Mannigfaltigkeit ist ein topologischer Raum , in dem es für jeden Punkt eine Umgebung gibt, die homöomorph zu einem Banachraum ist. (de) In mathematics, a Banach manifold is a manifold modeled on Banach spaces. Thus it is a topological space in which each point has a neighbourhood homeomorphic to an open set in a Banach space (a more involved and formal definition is given below). Banach manifolds are one possibility of extending manifolds to infinite dimensions. A further generalisation is to Fréchet manifolds, replacing Banach spaces by Fréchet spaces. On the other hand, a Hilbert manifold is a special case of a Banach manifold in which the manifold is locally modeled on Hilbert spaces. (en) En matemáticas, una variedad de Banach es una variedad modelada sobre espacios de Banach. Más concretamente, es un espacio topológico en el que cada punto tiene un entorno homeomorfo a un abierto de un espacio de Banach. Las variedades de Banach son una posibilidad de extender la noción de variedad a infinitas dimensiones. Una generalización aún más amplia se consigue con las , en las que se reemplazan los espacios de Banach por espacios de Fréchet. Por otro lado, una es un caso especial de variedad de Banach en el que la variedad es modelada localmente sobre espacios de Hilbert. (es)
dcterms:subject	Banach spaces Differential geometry Structures on manifolds Manifolds Generalized manifolds Nonlinear functional analysis
Wikipage page ID	2504397 (xsd:integer)
Wikipage revision ID	1115864249 (xsd:integer)
Link from a Wikipage to another Wikipage	Banach spaces Homeomorphic Differential geometry Structures on manifolds Continuous function Mathematics Neighbourhood (mathematics) Norm (mathematics) Operator norm Separable space Fréchet space Connected space Smooth function Embedding Fréchet derivative Fréchet manifold Banach spaces Topological vector space Topology Well-behaved Hausdorff space Manifolds Equivalence relation Generalized manifolds Nonlinear functional analysis Hilbert manifold Hilbert space Intersection (set theory) Isomorphic Atlas (topology) Bijection Homeomorphism Dimension Manifold Identity function Infinity Metric space Open set Set (mathematics) Union (set theory) Topological space Subset Open subset Derivative (generalizations) Closed subset dbr:Wiktionary:A_priori
sameAs	Banach manifold Banach manifold Banach manifold Banach manifold Banach manifold Banach manifold
dbp:wikiPageUsesTemplate	dbt:Banach_spaces dbt:Annotated_link dbt:Cite_book dbt:Cite_journal dbt:Em dbt:Reflist dbt:Short_description dbt:Analysis_in_topological_vector_spaces dbt:Functional_Analysis dbt:Manifolds
has abstract	Eine Banach-Mannigfaltigkeit ist ein topologischer Raum , in dem es für jeden Punkt eine Umgebung gibt, die homöomorph zu einem Banachraum ist. (de) In mathematics, a Banach manifold is a manifold modeled on Banach spaces. Thus it is a topological space in which each point has a neighbourhood homeomorphic to an open set in a Banach space (a more involved and formal definition is given below). Banach manifolds are one possibility of extending manifolds to infinite dimensions. A further generalisation is to Fréchet manifolds, replacing Banach spaces by Fréchet spaces. On the other hand, a Hilbert manifold is a special case of a Banach manifold in which the manifold is locally modeled on Hilbert spaces. (en) En matemáticas, una variedad de Banach es una variedad modelada sobre espacios de Banach. Más concretamente, es un espacio topológico en el que cada punto tiene un entorno homeomorfo a un abierto de un espacio de Banach. Las variedades de Banach son una posibilidad de extender la noción de variedad a infinitas dimensiones. Una generalización aún más amplia se consigue con las , en las que se reemplazan los espacios de Banach por espacios de Fréchet. Por otro lado, una es un caso especial de variedad de Banach en el que la variedad es modelada localmente sobre espacios de Hilbert. (es)
gold:hypernym	Manifold
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foaf:isPrimaryTopicOf	wikipedia-en:Banach_manifold
is Link from a Wikipage to another Wikipage of	List of differential geometry topics Integral curve

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