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In mathematics, a function between topological spaces is called proper if inverse images of compact subsets are compact. In algebraic geometry, the analogous concept is called a proper morphism.

Attributes	Values
rdf:type	yago:WikicatContinuousMappings yago:Abstraction100002137 yago:Function113783816 yago:MathematicalRelation113783581 yago:Relation100031921
rdfs:label	Eigentliche Abbildung (de) Application propre (fr) Funzione propria (it) 고유 함수 (ko) 固有写像 (ja) Proper map (en)
rdfs:comment	Eine eigentliche Abbildung ist eine stetige Abbildung, die in der mengentheoretischen Topologie, einem Teilgebiet der Mathematik, untersucht wird. (de) En mathématiques, une application est dite propre si elle vérifie une certaine propriété topologique. La définition la plus courante, valable pour une application continue d'un espace séparé dans un espace localement compact, est que l'application est propre si l'image réciproque de toute partie compacte de l'espace d'arrivée est compacte. Cette définition est équivalente, dans ce contexte, à la définition générale : une application (non nécessairement continue et entre espaces topologiques quelconques) est propre si elle est « universellement fermée ». (fr) In mathematics, a function between topological spaces is called proper if inverse images of compact subsets are compact. In algebraic geometry, the analogous concept is called a proper morphism. (en) ( 이 문서는 일반위상수학의 개념에 관한 것입니다. 대수기하학의 개념에 대해서는 고유 사상 문서를, 함수 공간에서의 고유벡터에 대해서는 고윳값과 고유 벡터 문서를 참고하십시오.) 일반위상수학에서 고유 함수(固有函數, 영어: proper map)은 콤팩트 집합의 원상이 콤팩트한 연속 함수이다. (ko) 数学において、位相空間の間のある函数が固有写像（こゆうしゃぞう、英: proper map）であるとは、コンパクト部分集合に対するその逆像がコンパクトであることをいう。代数幾何学において、類似の概念は固有射と呼ばれる。 (ja) In topologia una funzione continua fra spazi topologici è propria se la controimmagine di ogni insieme compatto è compatta. (it)
dcterms:subject	Continuous mappings
Wikipage page ID	1190262 (xsd:integer)
Wikipage revision ID	1112292263 (xsd:integer)
Link from a Wikipage to another Wikipage	Compact space Continuous map Convex analysis Mathematics Closed map Function (mathematics) Analogous Pointless topology Topology Hausdorff space Locally compact space Algebraic geometry Oxford University Press Proper morphism Continuous mappings Topos Metric space Journal of the London Mathematical Society First-countable space Inverse image Topological space Preimage Booksurge Springer-Verlag Compact set Compactly generated Hausdorff space Surjective map dbr:Locally_copact_space
sameAs	Proper map Proper map Proper map Proper map Proper map Proper map Proper map Proper map Proper map Proper map
dbp:wikiPageUsesTemplate	dbt:About dbt:Annotated_link dbt:Cite_book dbt:Cite_journal dbt:Em dbt:Harv dbt:Refbegin dbt:Refend dbt:Reflist dbt:Sfn dbt:Short_description dbt:Collapse_bottom dbt:Collapse_top dbt:Lee_Introduction_to_Smooth_Manifolds dbt:Topology
has abstract	Eine eigentliche Abbildung ist eine stetige Abbildung, die in der mengentheoretischen Topologie, einem Teilgebiet der Mathematik, untersucht wird. (de) En mathématiques, une application est dite propre si elle vérifie une certaine propriété topologique. La définition la plus courante, valable pour une application continue d'un espace séparé dans un espace localement compact, est que l'application est propre si l'image réciproque de toute partie compacte de l'espace d'arrivée est compacte. Cette définition est équivalente, dans ce contexte, à la définition générale : une application (non nécessairement continue et entre espaces topologiques quelconques) est propre si elle est « universellement fermée ». (fr) In mathematics, a function between topological spaces is called proper if inverse images of compact subsets are compact. In algebraic geometry, the analogous concept is called a proper morphism. (en) ( 이 문서는 일반위상수학의 개념에 관한 것입니다. 대수기하학의 개념에 대해서는 고유 사상 문서를, 함수 공간에서의 고유벡터에 대해서는 고윳값과 고유 벡터 문서를 참고하십시오.) 일반위상수학에서 고유 함수(固有函數, 영어: proper map)은 콤팩트 집합의 원상이 콤팩트한 연속 함수이다. (ko) 数学において、位相空間の間のある函数が固有写像（こゆうしゃぞう、英: proper map）であるとは、コンパクト部分集合に対するその逆像がコンパクトであることをいう。代数幾何学において、類似の概念は固有射と呼ばれる。 (ja) In topologia una funzione continua fra spazi topologici è propria se la controimmagine di ogni insieme compatto è compatta. (it)
prov:wasDerivedFrom	wikipedia-en:Proper_map?oldid=1112292263&ns=0
page length (characters) of wiki page	6965 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Proper_map
is Link from a Wikipage to another Wikipage of	End (topology) Lie groupoid Lift (mathematics) Compact space Function of several complex variables Submanifold Leray spectral sequence Haagerup property Local homeomorphism Local invariant cycle theorem Stein manifold Alexander–Spanier cohomology 3-manifold Fiber (mathematics) Fiber bundle Field (mathematics) Diffeomorphism Direct image with compact support

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