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countably complete

См. также в других словарях:

  • Complete metric space — Cauchy completion redirects here. For the use in category theory, see Karoubi envelope. In mathematical analysis, a metric space M is called complete (or Cauchy) if every Cauchy sequence of points in M has a limit that is also in M or,… …   Wikipedia

  • Complete theory — In mathematical logic, a theory is complete if it is a maximal consistent set of sentences, i.e., if it is consistent, and none of its proper extensions is consistent. For theories in logics which contain classical propositional logic, this is… …   Wikipedia

  • Ultrafilter — In the mathematical field of set theory, an ultrafilter on a set X is a collection of subsets of X that is a filter, that cannot be enlarged (as a filter). An ultrafilter may be considered as a finitely additive measure. Then every subset of X is …   Wikipedia

  • Sigma-ideal — In mathematics, particularly measure theory, a σ ideal of a sigma algebra ( σ , read sigma, means countable in this context) is a subset with certain desirable closure properties. It is a special type of ideal. Its most frequent application is… …   Wikipedia

  • Martin measure — In descriptive set theory, the Martin measure is a filter on the set of Turing degrees of sets of natural numbers. Under the axiom of determinacy it can be shown to be an ultrafilter. Definition Let D be the set of Turing degrees of sets of… …   Wikipedia

  • Boolean algebras canonically defined — Boolean algebras have been formally defined variously as a kind of lattice and as a kind of ring. This article presents them more neutrally but equally formally as simply the models of the equational theory of two values, and observes the… …   Wikipedia

  • Glossary of topology — This is a glossary of some terms used in the branch of mathematics known as topology. Although there is no absolute distinction between different areas of topology, the focus here is on general topology. The following definitions are also… …   Wikipedia

  • Standard probability space — In probability theory, a standard probability space (called also Lebesgue Rokhlin probability space) is a probability space satisfying certain assumptions introduced by Vladimir Rokhlin in 1940 [1] . He showed that the unit interval endowed with… …   Wikipedia

  • Hilbert space — For the Hilbert space filling curve, see Hilbert curve. Hilbert spaces can be used to study the harmonics of vibrating strings. The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It… …   Wikipedia

  • 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

  • Measure (mathematics) — Informally, a measure has the property of being monotone in the sense that if A is a subset of B, the measure of A is less than or equal to the measure of B. Furthermore, the measure of the empty set is required to be 0. In mathematical analysis …   Wikipedia

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