### Some articles on *closure operators, closure operator, operator, closure*:

Consequence Operator -

... A function cl P → P from a partial order P to itself is called a

**Closure Operators**On Partially Ordered Sets... A function cl P → P from a partial order P to itself is called a

**closure operator**if it satisfies the following axioms for all elements x, y in P ... k ≤ idP is called a kernel**operator**, interior**operator**, or dual**closure**... B, then the self-map on the powerset of B given by μA(X) = A ∪ X is a**closure operator**, whereas λA(X) = A ∩ X is a kernel**operator**...**Closure Operators**On Partially Ordered Sets

... A function cl P → P from a partial order P to itself is called a

**closure operator**if it satisfies the following axioms for all elements x, y in P ... k ≤ idP is called a kernel

**operator**, interior

**operator**, or dual

**closure**... if A is a subset of a set B, then the self-map on the powerset of B given by μA(X) = A ∪ X is a

**closure operator**, whereas λA(X) = A ∩ X is a kernel

**operator**...

Matroid - Definition -

... The

**Closure Operators**... The

**closure**of a subset of is the set ... This defines a**closure operator**where denotes the power set, with the following properties For all subsets of ... The first three of these properties are the defining properties of a**closure operator**...Consequence Operator

... In mathematics, a

... 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 (cl is ... by the sets of the form cl(X), since the**closure**cl(X) of a set X is the smallest closed set containing X ... Moore who studied**closure operators**in 1911 ...Main Site Subjects

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