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- Closure_operator abstract "In mathematics, a closure operator on a set S is a function from the power set of S to itself which satisfies the following conditions for all sets Closure operators are determined by their closed sets, i.e., by the sets of the form cl(X), since the closure cl(X) of a set X is the smallest closed set containing X. Such families of "closed sets" are sometimes called "Moore families", in honor of E. H. Moore who studied closure operators in 1911. Closure operators are also called "hull operators", which prevents confusion with the "closure operators" studied in topology. A set together with a closure operator on it is sometimes called a closure system.Closure operators have many applications: In topology, the closure operators are topological closure operators, which must satisfy for all (Note that for this gives ). In algebra and logic, many closure operators are finitary closure operators, i.e. they satisfy In universal logic, closure operators are also known as consequence operators. In the theory of partially ordered sets, which are important in theoretical computer science, closure operators have an alternative definition.".
- Closure_operator wikiPageExternalLink consequence-algebraic.
- Closure_operator wikiPageExternalLink gal_bw.ps.gz.
- Closure_operator wikiPageExternalLink primer.ps.
- Closure_operator wikiPageExternalLink ualg.html.
- Closure_operator wikiPageID "483120".
- Closure_operator wikiPageRevisionID "572369889".
- Closure_operator hasPhotoCollection Closure_operator.
- Closure_operator subject Category:Closure_operators.
- Closure_operator subject Category:Order_theory.
- Closure_operator subject Category:Universal_algebra.
- Closure_operator type Abstraction100002137.
- Closure_operator type ClosureOperators.
- Closure_operator type Function113783816.
- Closure_operator type MathematicalRelation113783581.
- Closure_operator type Operator113786413.
- Closure_operator type Relation100031921.
- Closure_operator comment "In mathematics, a closure operator on a set S is a function from the power set of S to itself which satisfies the following conditions for all sets Closure operators are determined by their closed sets, i.e., by the sets of the form cl(X), since the closure cl(X) of a set X is the smallest closed set containing X. Such families of "closed sets" are sometimes called "Moore families", in honor of E. H. Moore who studied closure operators in 1911.".
- Closure_operator label "Closure operator".
- Closure_operator label "Hüllenoperator".
- Closure_operator label "Оператор замыкания".
- Closure_operator label "闭包算子".
- Closure_operator sameAs Hüllenoperator.
- Closure_operator sameAs 폐포연산.
- Closure_operator sameAs m.02fxcq.
- Closure_operator sameAs Q10564851.
- Closure_operator sameAs Q10564851.
- Closure_operator sameAs Closure_operator.
- Closure_operator wasDerivedFrom Closure_operator?oldid=572369889.
- Closure_operator isPrimaryTopicOf Closure_operator.