Where does closure collide?

In topology, the closure of a set is the smallest closed set that contains it: equivalently, the set together with all of its limit points, the points every neighbourhood of which meets the set. Kuratowski's 1922 Sur l'opération Ā de l'Analysis Situs showed that this closure operator, obeying a short list of axioms, can serve as the primitive from which an entire topology is built. The referent is a precise operation on the subsets of a space, fixed by those axioms and yielding a unique result, and it has nothing to do with a mind seeking certainty, an eye completing a figure, or a group guarding its privileges.[1]

Unit

The smallest closed set containing a given set, produced by the closure operator

Recovery means

Not applicable

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Determined by proof from the closure axioms, or by taking the union of a set with its set of limit points

In social and cognitive psychology, the need for cognitive closure is a person's desire for a firm, definite answer to a question and a matching aversion to ambiguity and confusion. Webster and Kruglanski's 1994 Individual differences in need for cognitive closure introduced a scale that measures it as a stable individual difference, and traced how a high need pushes people to seize on early information and then freeze on a conclusion. The referent is a motivational state or trait inside a reasoning person, indexed by questionnaire, not an operation on a set, a rule of perception, or a strategy of social exclusion.[2]

Unit

A motivational disposition toward certainty, scored on the Need for Closure Scale

Recovery means

Not applicable

Measured by

Assessed by self-report questionnaire, chiefly the Need for Closure Scale, and by its effects on judgement under time pressure

In Gestalt psychology, the law of closure is the perceptual tendency to complete an incomplete or interrupted figure, so that a broken outline or a scatter of fragments is seen as one whole, closed shape. Wertheimer's 1923 Untersuchungen zur Lehre von der Gestalt set out the grouping principles by which the visual system organises separate elements into unified forms. The referent is an automatic principle of perceptual organisation in the seeing brain, studied with figures and displays, and it is unrelated to a topological operator, a felt need for certainty, or a group's control of resources.[3]

Unit

A perceptual grouping tendency that closes an incomplete figure into a whole form

Recovery means

Not applicable

Measured by

Demonstrated with fragmented or interrupted figures and studied through reports and judgements of what observers perceive

In sociology, social closure is the process by which a group secures advantages for itself by restricting access to resources and opportunities to a limited circle of eligibles, drawing a boundary that keeps outsiders out. Parkin's 1979 Marxism and Class Theory, developing a concept from Max Weber, analysed closure as strategies of exclusion and usurpation through which classes and status groups monopolise rewards. The referent is a collective social practice of boundary drawing and monopoly, studied through institutions, credentials, and membership, not a mathematical operation, a personal craving for certainty, or a law of vision.[4]

Unit

A collective strategy of exclusion that restricts access to resources and opportunities

Recovery means

Not applicable

Measured by

Traced through institutions, credentials, and membership rules, and through the inequalities that exclusion produces

In science and technology studies, closure refers to the point at which a controversy over a technology ends and its meaning stabilizes, as happened with the safety bicycle. This meaning comes from Pinch (1984) in Social Studies of Science.[5]

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In literary theory, closure refers to the way a poem signals its ending, so that a reader feels it to be complete and conclusive. This meaning comes from Smith (1968) in Poetic closure.[6]

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