# compactness

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**Compactness measure of a shape**— The compactness measure of a shape, sometimes called the shape factor, is a numerical quantity representing the degree to which a shape is compact. The meaning of compact here is not related to the topological notion of compact space. Various… …12

**compactness**— noun see compact I …13

**compactness**— noun the state of being compact …14

**compactness**— (Roget s Thesaurus II) noun The quality, condition, or degree of being thick: density, solidity, thickness. See THICK …15

**compactness**— com pactÂ·ness || nÉªs n. density, solidity …16

**compactness**— com·pact·ness …17

**compactness**— noun 1. the spatial property of being crowded together • Syn: ↑concentration, ↑density, ↑denseness, ↑tightness • Ant: ↑distribution (for: ↑concentration) …18

**compactness theorem**— Theorem stating that any collection of well formed formulae of a language has a model, if every finite subset of the collection has a model …19

**Mahler's compactness theorem**— In mathematics, Mahler s compactness theorem, proved by Kurt Mahler (1946), is a foundational result on lattices in Euclidean space, characterising sets of lattices that are bounded in a certain definite sense. Looked at another way, it… …20

**Measure of non-compactness**— In functional analysis, two measures of non compactness are commonly used; these associate numbers to sets in such a way that compact sets all get the measure 0, and other sets get measures that are bigger according to how far they are removed… …