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Glite Dictionary
🔒 Able to shut 📐 Can be closed
closable

closable

8.7
In math, an operator that you can extend to include all its limit values
  • adjective
  • /ˈkloʊzəbl/
  • Specialized
translation icon : cerrable
  • Mathematicians often check whether a given unbounded operator is closable before proceeding with further analysis.

Examples

  • If an operator is closable, its closure is unique and well-defined.

  • The operator defined on smooth functions is closable in the Hilbert space setting.

  • The operator is closable in this function space.

  • Is this operator closable under the given conditions?

  • In functional analysis, determining if an operator is closable is essential for its proper treatment.

  • Many operators studied in quantum mechanics are closable when defined on certain domains.

  • To ensure accurate results, one must verify that an operator is closable before applying it in a framework.

Synonyms

extendable
vsclosable
1 3.7

Can be made longer or larger

is a mathematical sense about extending an operator to a closed form

Surface Forms

closable positive

Morphology

closable = close (semi-transparent) = close + able

Formed from 'close' + '-able', but the mathematical sense depends on the technical notion of a 'closed' operator, which is specialized knowledge beyond general learners.

Etymology

The word closable in mathematics also comes from close, meaning 'to shut', and -able, meaning 'able to'. A helpful way to remember this use is to imagine an operator, a math rule, that can be 'closed' or completed. So a closable operator is 'able to be made closed', which is why the same idea of 'shutting' or 'finishing' explains the technical meaning.