About: Remmert–Stein theorem

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In complex analysis, a field in mathematics, the Remmert–Stein theorem, introduced by Reinhold Remmert and Karl Stein, gives conditions for the closure of an analytic set to be analytic. The theorem states that if F is an analytic set of dimension less than k in some complex manifold D, and M is an analytic subset of D – F with all components of dimension at least k, then the closure of M is either analytic or contains F.

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rdfs:label	Remmert–Stein theorem (en) Remmert–Steins sats (sv)
rdfs:comment	Inom komplex analys, en del av matematiken, är Remmert–Steins sats, introducerad av och, ett resultat som ger krav för slutna höljet av en att vara analytisk. Satsen säger att om F är en analytisk mängd med dimension mindre än k i någon D, och M är en analytisk delmängd av D – F med alla komponenter av dimension minst k, då är slutna höljet av M antingen analytiskt eller innehåller F. Kravet om dimensionerna är nödvändigt: exempelvis är mängden av punkter 1/n i komplexa planet analytisk i komplexa planet minus origo, men dess slutna hölje i komplexa planet är inte. (sv) In complex analysis, a field in mathematics, the Remmert–Stein theorem, introduced by Reinhold Remmert and Karl Stein, gives conditions for the closure of an analytic set to be analytic. The theorem states that if F is an analytic set of dimension less than k in some complex manifold D, and M is an analytic subset of D – F with all components of dimension at least k, then the closure of M is either analytic or contains F. (en)
dcterms:subject	Complex manifolds Theorems in complex analysis
Wikipage page ID	37670745 (xsd:integer)
Wikipage revision ID	1113169924 (xsd:integer)
Link from a Wikipage to another Wikipage	Complex manifolds Complex analysis Complex plane Analytic space Closure (topology) Analytic variety Complex manifold Mathematische Annalen Algebraic geometry and analytic geometry Theorems in complex analysis Projective algebraic variety dbr:Proper_mapping_theorem
sameAs	Remmert–Stein theorem Remmert–Stein theorem Remmert–Stein theorem Remmert–Stein theorem
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Cite_journal dbt:Harvtxt dbt:Harvs dbt:Analysis-stub
first	Karl (en) Reinhold (en)
last	Stein (en) Remmert (en)
year	1953 (xsd:integer)
has abstract	In complex analysis, a field in mathematics, the Remmert–Stein theorem, introduced by Reinhold Remmert and Karl Stein, gives conditions for the closure of an analytic set to be analytic. The theorem states that if F is an analytic set of dimension less than k in some complex manifold D, and M is an analytic subset of D – F with all components of dimension at least k, then the closure of M is either analytic or contains F. The condition on the dimensions is necessary: for example, the set of points (1/n,0) in the complex plane is analytic in the complex plane minus the origin, but its closure in the complex plane is not. (en) Inom komplex analys, en del av matematiken, är Remmert–Steins sats, introducerad av och, ett resultat som ger krav för slutna höljet av en att vara analytisk. Satsen säger att om F är en analytisk mängd med dimension mindre än k i någon D, och M är en analytisk delmängd av D – F med alla komponenter av dimension minst k, då är slutna höljet av M antingen analytiskt eller innehåller F. Kravet om dimensionerna är nödvändigt: exempelvis är mängden av punkter 1/n i komplexa planet analytisk i komplexa planet minus origo, men dess slutna hölje i komplexa planet är inte. (sv)
author1-link	Reinhold Remmert (en)
author2-link	Karl Stein (en)
gold:hypernym	Set
prov:wasDerivedFrom	wikipedia-en:Remmert–Stein_theorem?oldid=1113169924&ns=0
page length (characters) of wiki page	2309 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Remmert–Stein_theorem
is Link from a Wikipage to another Wikipage of	Reinhold Remmert Remmert-Stein theorem Karl Stein (mathematician) List of theorems
is Wikipage redirect of	Remmert-Stein theorem
is known for of	Karl Stein (mathematician)
is known for of	Karl Stein (mathematician)
is foaf:primaryTopic of	wikipedia-en:Remmert–Stein_theorem

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