closure operator

== English == === Noun === closure operator (plural closure operators) (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: u ( U ∪ B ) = u U ∪ u B , A ⊂ u ( A ) , u ∅ = ∅ {\displaystyle u(U\cup B)=uU\cup uB,A\subset u(A),u\emptyset =\emptyset } . ==== Derived terms ==== ==== Related terms ==== ==== Translations ====