e/Closure operator

Information
has gloss	eng: In mathematics, a closure operator on a set S is a function cl: P(S) → P(S) from the power set of S to itself which satisfies the following conditions for all sets X,Y ⊆ S. :\| border="0" \|- \| X ⊆ cl(X) \| (cl is extensive) \|- \| X ⊆ Y implies cl(X) ⊆ cl(Y) \| (cl is increasing) \|- \| cl(cl(X)) = cl(X) \| (cl is idempotent) \|}
lexicalization	eng: Closure operators
lexicalization	eng: closure operator
subclass of	(noun) (mathematics) a symbol or function representing a mathematical operation operator
has instance	e/Approach space
has instance	e/Closure (mathematics)
has instance	e/Closure (topology)
has instance	e/Cylindric algebra
has instance	e/Galois connexion
has instance	e/Idempotence
has instance	e/Interior algebra
has instance	e/Monadic Boolean algebra
has instance	e/P closure
has instance	e/Preclosure operator
has instance	e/Proximity space
has instance	e/Reflexive closure
has instance	e/Reflexive transitive closure
has instance	e/Reflexive transitive symmetric closure
has instance	e/Sequential closure operator
has instance	e/Symmetric closure
has instance	e/Transitive closure

Meaning
Hungarian
lexicalization	hun: Lezárási operátor
Korean
lexicalization	kor: 닫힘 연산
Polish
has gloss	pol: Operator konsekwencji - pojęcie wprowadzone do logiki przez Alfreda Tarskiego. Motywacją dla jego wprowadzenia była formalizacja pojęcia konsekwencji określonego zbioru przesłanek.
lexicalization	pol: operator konsekwencji
Russian
has gloss	rus: Оператор замыкания — обобщение интуитивной концепции замыкания. Именно: если \langle P, \leqslant\rangle — частично упорядоченное множество, оператор C: P\to P будет называться оператором замыкания, если выполнены три условия:
lexicalization	rus: Оператор замыкания
Chinese
has gloss	zho: 在数学中，给定偏序集合 (P, ≤)，在 P 上的闭包算子是函数 C : P → P 带有如下性质: x ≤ C(x) 对于所有 x，就是说 C 是扩展性的。如果 x ≤ y，则 C(x) ≤ C(y)，就是 C 是单调递增的。 *C(C(x)) = C(x) 对于所有的 x，就是说 C 是幂等函数。
lexicalization	zho: 闭包算子