About: Constructible set (topology)

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In topology, constructible sets are a class of subsets of a topological space that have a relatively "simple" structure.They are used particularly in algebraic geometry and related fields. A key result known as Chevalley's theoremin algebraic geometry shows that the image of a constructible set is constructible for an important class of mappings(more specifically morphisms) of algebraic varieties (or more generally schemes).In addition, a large number of "local" geometric properties of schemes, morphisms and sheaves are (locally) constructible.Constructible sets also feature in the definition of various types of constructible sheaves in algebraic geometryand intersection cohomology.

Attributes	Values
rdf:type	Thing
rdfs:label	Konstruierbare Menge (Topologie) (de) Constructible set (topology) (en) Partie constructible (fr)
rdfs:comment	In topology, constructible sets are a class of subsets of a topological space that have a relatively "simple" structure.They are used particularly in algebraic geometry and related fields. A key result known as Chevalley's theoremin algebraic geometry shows that the image of a constructible set is constructible for an important class of mappings(more specifically morphisms) of algebraic varieties (or more generally schemes).In addition, a large number of "local" geometric properties of schemes, morphisms and sheaves are (locally) constructible.Constructible sets also feature in the definition of various types of constructible sheaves in algebraic geometryand intersection cohomology. (en) Eine konstruierbare Menge ist eine spezielle Teilmenge eines topologischen Raumes und damit ein Objekt aus der Topologie, einem Teilgebiet der Mathematik. Konstruierbare Mengen werden vor allem in der algebraischen Geometrie betrachtet. (de) En géométrie algébrique, la notion de partie constructible généralise les parties ouvertes, fermées et même localement fermées. Les ensembles constructibles ont été introduits par Claude Chevalley, et présentent l'avantage d'être d'une manipulation plus souple. Par exemple l'image d'un constructible par un morphisme de présentation finie est constructible, alors ce n'est pas vrai pour les parties ouvertes ou fermées. Mais surtout, sous des hypothèses assez générales, si est un morphisme de schémas, l'ensemble des points de X ou de Y vérifiant certains types de propriétés est un ensemble constructible (sans être ni ouvert ni fermé en général). (fr)
dcterms:subject	Topology Algebraic geometry
Wikipage page ID	23234121 (xsd:integer)
Wikipage revision ID	1114976873 (xsd:integer)
Link from a Wikipage to another Wikipage	Quasicoherent sheaf Morphism of schemes Noetherian space Compact space Complement (set theory) Glossary of algebraic geometry Constructible sheaf Constructible topology Closed set Dense set Stacks Project Topology Algebraic geometry Algebraic varieties Algebraic variety Topology Flat morphism Intersection (set theory) Cover (topology) Armand Borel Algebraic geometry Open set Map (mathematics) Scheme (mathematics) Union (set theory) Image (mathematics) Topological space Éléments de géométrie algébrique Intersection cohomology Springer-Verlag Polish Scientific Publishers Locally closed set Locally noetherian topological space
Link from a Wikipage to an external page	https://stacks.math.columbia.edu/tag/04ZC https://stacks.math.columbia.edu/tag/054H https://web.archive.org/web/*/http:/www.lri.fr/~allouche/allouche96e.ps
sameAs	Constructible set (topology) Constructible set (topology) Constructible set (topology) Constructible set (topology) Constructible set (topology)
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has abstract	In topology, constructible sets are a class of subsets of a topological space that have a relatively "simple" structure.They are used particularly in algebraic geometry and related fields. A key result known as Chevalley's theoremin algebraic geometry shows that the image of a constructible set is constructible for an important class of mappings(more specifically morphisms) of algebraic varieties (or more generally schemes).In addition, a large number of "local" geometric properties of schemes, morphisms and sheaves are (locally) constructible.Constructible sets also feature in the definition of various types of constructible sheaves in algebraic geometryand intersection cohomology. (en) Eine konstruierbare Menge ist eine spezielle Teilmenge eines topologischen Raumes und damit ein Objekt aus der Topologie, einem Teilgebiet der Mathematik. Konstruierbare Mengen werden vor allem in der algebraischen Geometrie betrachtet. (de) En géométrie algébrique, la notion de partie constructible généralise les parties ouvertes, fermées et même localement fermées. Les ensembles constructibles ont été introduits par Claude Chevalley, et présentent l'avantage d'être d'une manipulation plus souple. Par exemple l'image d'un constructible par un morphisme de présentation finie est constructible, alors ce n'est pas vrai pour les parties ouvertes ou fermées. Mais surtout, sous des hypothèses assez générales, si est un morphisme de schémas, l'ensemble des points de X ou de Y vérifiant certains types de propriétés est un ensemble constructible (sans être ni ouvert ni fermé en général). (fr)
prov:wasDerivedFrom	wikipedia-en:Constructible_set_(topology)?oldid=1114976873&ns=0
page length (characters) of wiki page	10716 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Constructible_set_(topology)
is Link from a Wikipage to another Wikipage of	Morphism of schemes Retrocompact Integral element Claude Chevalley Glossary of commutative algebra Morphism of algebraic varieties Constructibility Constructible topology Chevalley theorem Locally closed subset Algebraic variety Constructible set Veronese surface Retrocompact set Chevalley's theorem on constructible sets
is Wikipage redirect of	Retrocompact Retrocompact set Chevalley's theorem on constructible sets
is Wikipage disambiguates of	Constructible set
is foaf:primaryTopic of	wikipedia-en:Constructible_set_(topology)

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