About: Analytic manifold

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In mathematics, an analytic manifold, also known as a manifold, is a differentiable manifold with analytic transition maps. The term usually refers to real analytic manifolds, although complex manifolds are also analytic. In algebraic geometry, analytic spaces are a generalization of analytic manifolds such that singularities are permitted. For , the space of analytic functions, , consists of infinitely differentiable functions , such that the Taylor series

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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	Analytic manifold (en) 解析流形 (zh) Аналітичний многовид (uk)
rdfs:comment	在數學中，一個解析流形（有時也記作流形）是一個拓撲流形配上一族坐標鄰域，使得坐標轉換都是實解析映射。 (zh) Аналіти́чний многови́д — це многовид з аналітичними функціями переходу. (uk) In mathematics, an analytic manifold, also known as a manifold, is a differentiable manifold with analytic transition maps. The term usually refers to real analytic manifolds, although complex manifolds are also analytic. In algebraic geometry, analytic spaces are a generalization of analytic manifolds such that singularities are permitted. For , the space of analytic functions, , consists of infinitely differentiable functions , such that the Taylor series (en)
dct:subject	Structures on manifolds Manifolds
Wikipage page ID	3183798 (xsd:integer)
Wikipage revision ID	1115832923 (xsd:integer)
Link from a Wikipage to another Wikipage	Structures on manifolds Analytic function Analytic space Mathematics Analytic variety Complex manifold Partition of unity Smoothness Manifolds Differentiable manifold
sameAs	Analytic manifold Analytic manifold Analytic manifold Analytic manifold Analytic manifold Analytic manifold
dbp:wikiPageUsesTemplate	dbt:Reflist dbt:Slink dbt:Being_merged dbt:Topology-stub
has abstract	In mathematics, an analytic manifold, also known as a manifold, is a differentiable manifold with analytic transition maps. The term usually refers to real analytic manifolds, although complex manifolds are also analytic. In algebraic geometry, analytic spaces are a generalization of analytic manifolds such that singularities are permitted. For , the space of analytic functions, , consists of infinitely differentiable functions , such that the Taylor series converges to in a neighborhood of , for all . The requirement that the transition maps be analytic is significantly more restrictive than that they be infinitely differentiable; the analytic manifolds are a proper subset of the smooth, i.e. , manifolds. There are many similarities between the theory of analytic and smooth manifolds, but a critical difference is that analytic manifolds do not admit analytic partitions of unity, whereas smooth partitions of unity are an essential tool in the study of smooth manifolds. A fuller description of the definitions and general theory can be found at differentiable manifolds, for the real case, and at complex manifolds, for the complex case. (en) 在數學中，一個解析流形（有時也記作流形）是一個拓撲流形配上一族坐標鄰域，使得坐標轉換都是實解析映射。 (zh) Аналіти́чний многови́д — це многовид з аналітичними функціями переходу. (uk)
gold:hypernym	Manifold
prov:wasDerivedFrom	wikipedia-en:Analytic_manifold?oldid=1115832923&ns=0
page length (characters) of wiki page	2820 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Analytic_manifold
is Link from a Wikipage to another Wikipage of	Projective space Rotation matrix Derivative of the exponential map Algebraic analysis Ricci-flat manifold List of manifolds Pseudogroup (G,X)-manifold Analytic space Smooth structure Andrew M. Gleason Analytic M. S. Narasimhan Partition of unity Stalk (sheaf) Category of manifolds Euclidean space Foliation Diffeology Harmonic coordinates Manifold Real coordinate space Projectively extended real line Long line (topology) Manifold (disambiguation) Singular point of an algebraic variety Unit disk Real-analytic manifold
is Wikipage redirect of	Real-analytic manifold
is Wikipage disambiguates of	Analytic Manifold (disambiguation)
is foaf:primaryTopic of	wikipedia-en:Analytic_manifold

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