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limit ultrafilter

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  • Banach limit — In mathematical analysis, a Banach limit is a continuous linear functional phi: ell infty o mathbb{R} defined on the Banach space ell infty of all bounded complex valued sequences such that for any sequences x=(x n) and y=(y n), the following… …   Wikipedia

  • Ultralimit — For the direct limit of a sequence of ultrapowers, see Ultraproduct. In mathematics, an ultralimit is a geometric construction that assigns to a sequence of metric spaces Xn a limiting metric space. The notion of an ultralimit captures the… …   Wikipedia

  • Filter (mathematics) — The powerset algebra of the set {1,2,3,4} with the upset colored green. The green elements make a principal ultrafilter on the lattice. In mathematics, a filter is a special subset of a partially ordered set. A frequently used special case is the …   Wikipedia

  • Hyperreal number — *R redirects here. For R*, see Rockstar Games. The system of hyperreal numbers represents a rigorous method of treating the infinite and infinitesimal quantities. The hyperreals, or nonstandard reals, *R, are an extension of the real numbers R… …   Wikipedia

  • Ultraproduct — An ultraproduct is a mathematical construction, of which the ultrapower (defined below) is a special case. Ultraproducts are used in abstract algebra to construct new fields from given ones, and in model theory, a branch of mathematical logic. In …   Wikipedia

  • Stone–Čech compactification — In the mathematical discipline of general topology, Stone–Čech compactification is a technique for constructing a universal map from a topological space X to a compact Hausdorff space beta; X . The Stone–Čech compactification beta; X of a… …   Wikipedia

  • PCF theory — is the name of a mathematical theory, introduced by Saharon Shelah (1978), that deals with the cofinality of the ultraproducts of ordered sets. It gives strong upper bounds on the cardinalities of power sets of singular cardinals, and has… …   Wikipedia

  • Tychonoff's theorem — For other theorems named after Tychonoff, see Tychonoff s theorem (disambiguation). In mathematics, Tychonoff s theorem states that the product of any collection of compact topological spaces is compact. The theorem is named after Andrey… …   Wikipedia

  • Boolean-valued model — In mathematical logic, a Boolean valued model is a generalization of the ordinary Tarskian notion of structure or model, in which the truth values of propositions are not limited to true and false , but take values in some fixed complete Boolean… …   Wikipedia

  • Measurable cardinal — In mathematics, a measurable cardinal is a certain kind of large cardinal number. Contents 1 Measurable 2 Real valued measurable 3 See also 4 References …   Wikipedia

  • List of order topics — This is a list of order topics, by Wikipedia page.An alphabetical list of many notions of order theory can be found in the order theory glossary. See also inequality, extreme value, optimization (mathematics), domain theory.Basic… …   Wikipedia

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