About: Kernel (set theory)

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In set theory, the kernel of a function (or equivalence kernel) may be taken to be either * the equivalence relation on the function's domain that roughly expresses the idea of "equivalent as far as the function can tell", or * the corresponding partition of the domain. An unrelated notion is that of the kernel of a non-empty family of sets which by definition is the intersection of all its elements: This definition is used in the theory of filters to classify them as being free or principal.

Attributes	Values
rdf:type	Thing
rdfs:label	Kernel (teoría de conjuntos) (es) Kernel (set theory) (en) Jądro (teoria mnogości) (pl)
rdfs:comment	En la teoría de conjuntos, el kernel o núcleo de una función f puede tomarse como: * La relación de equivalencia en el dominio de la función que expresa aproximadamente la idea de "equivalente en la medida en que la función f puede decir", o * La partición correspondiente del dominio. (es) In set theory, the kernel of a function (or equivalence kernel) may be taken to be either * the equivalence relation on the function's domain that roughly expresses the idea of "equivalent as far as the function can tell", or * the corresponding partition of the domain. An unrelated notion is that of the kernel of a non-empty family of sets which by definition is the intersection of all its elements: This definition is used in the theory of filters to classify them as being free or principal. (en) Jądro (zazwyczaj oznaczane ) - dla dowolnego przekształcenia jest to relacja równoważności zadana przez warunek: Alternatywna (równoważna) definicja jest następująca: gdzie oznacza złożenie relacji, a jest relacją odwrotną do (pl)
rdfs:seeAlso	Kernel (algebra) Topology Filters
dcterms:subject	Basic concepts in set theory Set theory Topology Abstract algebra
Wikipage page ID	330095 (xsd:integer)
Wikipage revision ID	1102147643 (xsd:integer)
Link from a Wikipage to another Wikipage	Cartesian product Binary relation Algebraic structure Basic concepts in set theory Homomorphism Vector space Intersection Compact space Continuous function Quotient (universal algebra) Quotient set Function (mathematics) Congruence relation Equivalence class Closed set Empty set Ideal (ring theory) Set theory Domain of a function Hausdorff space Topology Equivalence relation Filter (set theory) Finite intersection property Partition of a set Family of sets Isomorphism First isomorphism theorem Quotient space (topology) Group (mathematics) Ring (algebra) Abstract algebra Bijection Coimage Natural isomorphism Set (mathematics) Set theory Image (mathematics) Space (mathematics) Subset Principal filter Equal (math) Free filter
sameAs	Kernel (set theory) Kernel (set theory) Kernel (set theory) Kernel (set theory) Kernel (set theory)
dbp:wikiPageUsesTemplate	dbt:Annotated_link dbt:Cite_book dbt:Em dbt:Other_uses dbt:Refimprove dbt:Reflist dbt:See_also dbt:Sfn dbt:Short_description dbt:Visible_anchor dbt:Dolecki_Mynard_Convergence_Foundations_Of_Topology
has abstract	En la teoría de conjuntos, el kernel o núcleo de una función f puede tomarse como: * La relación de equivalencia en el dominio de la función que expresa aproximadamente la idea de "equivalente en la medida en que la función f puede decir", o * La partición correspondiente del dominio. (es) In set theory, the kernel of a function (or equivalence kernel) may be taken to be either * the equivalence relation on the function's domain that roughly expresses the idea of "equivalent as far as the function can tell", or * the corresponding partition of the domain. An unrelated notion is that of the kernel of a non-empty family of sets which by definition is the intersection of all its elements: This definition is used in the theory of filters to classify them as being free or principal. (en) Jądro (zazwyczaj oznaczane ) - dla dowolnego przekształcenia jest to relacja równoważności zadana przez warunek: Alternatywna (równoważna) definicja jest następująca: gdzie oznacza złożenie relacji, a jest relacją odwrotną do (pl)
prov:wasDerivedFrom	wikipedia-en:Kernel_(set_theory)?oldid=1102147643&ns=0
page length (characters) of wiki page	6819 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Kernel_(set_theory)
is Link from a Wikipage to another Wikipage of	Monoid ring Ultrafilter (set theory) Kriging Dobiński's formula Semigroup Isomorphism theorems BRST quantization Transversal (combinatorics) Krein–Milman theorem Metric tensor Kernel Kernel (function) Kernel of a family of sets Kernel of a function
is Wikipage redirect of	Kernel (function) Kernel of a family of sets Kernel of a function
is Wikipage disambiguates of	Kernel
is foaf:primaryTopic of	wikipedia-en:Kernel_(set_theory)

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