compactness

Noun

Meaning

The state or quality of being compact; close union of parts; density.

Source: Webster's dictionary

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Examples

Although the weak topology of the unit ball is not metrizable in general, one can characterize weak compactness using sequences. Source: Internet

Chennai-based NeoMotion, who won second place, makes bespoke wheelchairs, designed to ensure accurate posture, energy conservation and compactness to enhance accessibility and mobility. Source: Internet

Definitions Various definitions of compactness may apply, depending on the level of generality. Source: Internet

Closed sets also give a useful characterization of compactness: a topological space X is compact if and only if every collection of nonempty closed subsets of X with empty intersection admits a finite subcollection with empty intersection. Source: Internet

Conversely, for many deductive systems, it is possible to prove the completeness theorem as an effective consequence of the compactness theorem. Source: Internet

Finally, some questions arising from model theory (such as compactness for infinitary logics) have been shown to be equivalent to large cardinal axioms. Source: Internet

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