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The term closure is often used as a synonym for anonymous function, though strictly, an anonymous function is a function literal without a name, while a closure is an instance of a function, a value, whose non-local variables have been bound either to values or to storage locations (depending on the language; see the lexical environment section below).
An example is the topological closure operator; in Kuratowski's characterization, axioms K2, K3, K4' correspond to the above defining properties. An example not operating on subsets is the ceiling function, which maps every real number x to the smallest integer that is not smaller than x.
The transitive closure of this relation is a different relation, namely "there is a sequence of direct flights that begins at city x and ends at city y". Every relation can be extended in a similar way to a transitive relation. An example of a non-transitive relation with a less meaningful transitive closure is "x is the day of the week after y".
The forthcoming closure of the Grangemouth oil refinery is a “shining example of how not to do anything”, MPs were told as the boss of plant owners Ineos came under fire.
The separable closure is the full algebraic closure if and only if K is a perfect field. For example, if K is a field of characteristic p and if X is transcendental over K, () () is a non-separable algebraic field extension.
The closure of a set also depends upon in which space we are taking the closure. For example, if is the set of rational numbers, with the usual relative topology induced by the Euclidean space , and if = {: >, >}, then is both closed and open in because neither nor its complement can contain , which would be the lower bound of , but cannot be ...
The need for closure in social psychology is thought to be a fairly stable dispositional characteristic that can, nonetheless, be affected by situational factors. The Need for Closure Scale (NFCS) was developed by Arie Kruglanski, Donna Webster, and Adena Klem in 1993 and is designed to operationalize this construct and is presented as a unidimensional instrument possessing strong discriminant ...
Lambda lifting and closure are both methods for implementing block structured programs. It implements block structure by eliminating it. All functions are lifted to the global level. Closure conversion provides a "closure" which links the current frame to other frames. Closure conversion takes less compile time.