Closure Operators

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

Consequence 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 ... 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 - 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 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 ...