# closure

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## closure

1. Politics (in a deliberative body) a procedure by which debate may be halted and an immediate vote taken
2. Geology the vertical distance between the crest of an anticline and the lowest contour that surrounds it
3. Logic the closed sentence formed from a given open sentence by prefixing universal or existential quantifiers to bind all its free variables
4. Maths the smallest closed set containing a given set
5. Psychol the tendency, first noted by Gestalt psychologists, to see an incomplete figure like a circle with a gap in it as more complete than it is

## closure

[′klō·zhər]
(civil engineering)
(geology)
The vertical distance between the highest and lowest point on an anticline which is enclosed by contour lines.
(mathematics)
The union of a set and its cluster points; the smallest closed set containing the set.
Property of a mathematical set such that a specified mathematical operation that is applied to elements of the set produces only elements of the same set

## closure

(programming)
In a reduction system, a closure is a data structure that holds an expression and an environment of variable bindings in which that expression is to be evaluated. The variables may be local or global. Closures are used to represent unevaluated expressions when implementing functional programming languages with lazy evaluation. In a real implementation, both expression and environment are represented by pointers.

A suspension is a closure which includes a flag to say whether or not it has been evaluated. The term "thunk" has come to be synonymous with "closure" but originated outside functional programming.

## closure

(theory)
In domain theory, given a partially ordered set, D and a subset, X of D, the upward closure of X in D is the union over all x in X of the sets of all d in D such that x <= d. Thus the upward closure of X in D contains the elements of X and any greater element of D. A set is "upward closed" if it is the same as its upward closure, i.e. any d greater than an element is also an element. The downward closure (or "left closure") is similar but with d <= x. A downward closed set is one for which any d less than an element is also an element.

("<=" is written in LaTeX as \subseteq and the upward closure of X in D is written \uparrow_\D X).
References in periodicals archive ?
Innovation in plastic closures continues to be of growing interest, holding great potential for development in the future.
The Prince Albert pulp and paper mill in Saskatchewan, announced in October as an indefinite closure.
Leg cuff with front closure tie, allowing more comfortable closure on the outside of the boot collar
HEART AND HOLE In contrast to drugs, PFO closure appears highly effective against migraines and usually has no side effects, says Reisman, who has repaired the defect in more than 100 people.
This study uses a multiple time-series design to examine the impact of hospital closures on Medicare utilization and expenditures (Campbell and Stanley, 1963).
The following rival null hypothesis was tested as a preliminary measure: There are no differences in total number of closures and number of closures of persons with severe disabilities among counselors with different levels of education.
For us, the expansion of the 'Aluminium Closures--Turn 360 ' campaign from wine to include bottled products such as spirits; oils and vinegars; water and beverages is the next logical step in reinforcing the high-performance closure concept.
achieve higher competitive closure rates and lower numbers of non-competitive closures) but also more cost-efficient (i.

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