In mathematics, a closure operator on a set S is a function from the power set of S to itself that satisfies the following conditions for all sets
(cl is extensive),
(cl is increasing),
(cl is idempotent).
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 closure systems or "Moore families".[1] A set together with a closure operator on it is sometimes called a closure space. Closure operators are also called "hull operators", which prevents confusion with the "closure operators" studied in topology.
^Diatta, Jean (2009-11-14). "On critical sets of a finite Moore family". Advances in Data Analysis and Classification. 3 (3): 291–304. doi:10.1007/s11634-009-0053-8. ISSN 1862-5355. S2CID 26138007.
In mathematics, a closureoperator on a set S is a function cl : P ( S ) → P ( S ) {\displaystyle \operatorname {cl} :{\mathcal {P}}(S)\rightarrow {\mathcal...
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