compactness property

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• Compactness theorem — In mathematical logic, the compactness theorem states that a set of first order sentences has a model if and only if every finite subset of it has a model. This theorem is an important tool in model theory, as it provides a useful method for… …   Wikipedia

• compactness — See compactly. * * * ▪ mathematics       in mathematics, property of some topological spaces (a generalization of Euclidean space) that has its main use in the study of functions defined on such spaces. An open covering of a space (or set) is a… …   Universalium

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

• Finite intersection property — In general topology, the finite intersection property is a property of a collection of subsets of a set X . A collection has this property if the intersection over any finite subcollection of the collection is nonempty.DefinitionLet X be a set… …   Wikipedia

• Hereditary property — In mathematics, a hereditary property is a property of an object, that inherits to all its subobjects, where the term subobject depends on the context. These properties are particularly considered in topology and graph theory. Contents 1 In… …   Wikipedia

• Topological property — In topology and related areas of mathematics a topological property or topological invariant is a property of a topological space which is invariant under homeomorphisms. That is, a property of spaces is a topological property if whenever a space …   Wikipedia

• Uniform property — In the mathematical field of topology a uniform property or uniform invariant is a property of a uniform space which is invariant under uniform isomorphisms.Since uniform spaces come are topological spaces and uniform isomorphisms are… …   Wikipedia

• sequential compactness — noun The property of a metric space that every sequence has a convergent subsequence …   Wiktionary

• Compact space — Compactness redirects here. For the concept in first order logic, see compactness theorem. In mathematics, specifically general topology and metric topology, a compact space is an abstract mathematical space whose topology has the compactness… …   Wikipedia

• Strongly compact cardinal — In mathematical set theory, a strongly compact cardinal is a certain kind of large cardinal number; their existence can neither be proven nor disproven from the standard axioms of set theory.A cardinal kappa; is strongly compact if and only if… …   Wikipedia

• metalogic — /met euh loj ik/, n. the logical analysis of the fundamental concepts of logic. [1835 45; META + LOGIC] * * * Study of the syntax and the semantics of formal languages and formal systems. It is related to, but does not include, the formal… …   Universalium