In mathematics, a closure operator on a set S is a function cl : P ( S ) → P ( S ) {\displaystyle \operatorname {cl} :{\mathcal {P}}(S)\rightarrow {\mathcal...

operations individually. The closure of a subset is the result of a closure operator applied to the subset. The closure of a subset under some operations...

interior operator. Let X {\displaystyle X} be an arbitrary set and ℘ ( X ) {\displaystyle \wp (X)} its power set. A Kuratowski closure operator is a unary...

abstract theory of closure operators and the Kuratowski closure axioms can be readily translated into the language of interior operators by replacing sets...

that }}s_{\bullet }\to x\right\}} which defines a map, the sequential closure operator, on the power set of X . {\displaystyle X.} If necessary for clarity...

axioms for its use in database theory Closure (mathematics), the result of applying a closure operator Closure (topology), for a set, the smallest closed...

The convex hull operator is an example of a closure operator, and every antimatroid can be represented by applying this closure operator to finite sets...

functional analysis and operator theory, the notion of unbounded operator provides an abstract framework for dealing with differential operators, unbounded observables...

interior operator is the closure operator C defined by xC = ((x′)I)′. xC is called the closure of x. By the principle of duality, the closure operator satisfies...

abstract algebra (in particular, in the theory of projectors and closure operators) and functional programming (in which it is connected to the property...