closure operator

English

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closure operator

Wikipedia

Noun

closure operator (plural closure operators)

1. (mathematics, topology, algebra, "on" a set S) A function which maps any subset X of S onto another such subset (or possibly X itself) called the closure of X (thus providing a mathematical means to define closure).

   Synonym: hull operator (in contexts where the closure can be interpreted as an enclosing structure)

   Hyponyms: algebraic closure operator, topological closure operator

   • 1997 [Kluwer Academic], R. Friĉ, History of Sequential Convergence Spaces, C. E. Aull, R. Lowen (editors), Handbook of the History of General Topology, Volume 1, Springer, page 346,

     Let u be a closure operator on X satisfying the first three closure axioms: ${\displaystyle u(U\cup B)=uU\cup uB,A\subset u(A),u\emptyset =\emptyset }$.

Derived terms

• algebraic closure operator
• topological closure operator

Related terms

• closure axiom
• closure space
• closure system

Translations

function mapping a subset to its closure

French: please add this translation if you can German: Hüllenoperator m Italian: please add this translation if you can