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topology of uniform convergence

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  • Uniform convergence — In the mathematical field of analysis, uniform convergence is a type of convergence stronger than pointwise convergence. A sequence {fn} of functions converges uniformly to a limiting function f if the speed of convergence of fn(x) to f(x) does… …   Wikipedia

  • Uniform topology — In mathematics, the uniform topology on a space has several different meanings depending on the context:* In functional analysis, it sometimes refers to a polar topology on a topological vector space. * In general topology, it is the topology… …   Wikipedia

  • Convergence in measure — can refer to two distinct mathematical concepts which both generalize the concept of convergence in probability. Contents 1 Definitions 2 Properties 3 Counterexamples 4 Topology …   Wikipedia

  • Uniform space — In the mathematical field of topology, a uniform space is a set with a uniform structure. Uniform spaces are topological spaces with additional structure which is used to define uniform properties such as completeness, uniform continuity and… …   Wikipedia

  • Uniform norm — This article is about the function space norm. For the finite dimensional vector space distance, see Chebyshev distance. The black square is the set of points in R2 where the sup norm equals a fixed non zero constant. In mathematical analysis,… …   Wikipedia

  • Weak topology — This article discusses the weak topology on a normed vector space. For the weak topology induced by a family of maps see initial topology. For the weak topology generated by a cover of a space see coherent topology. In mathematics, weak topology… …   Wikipedia

  • Dual topology — In functional analysis and related areas of mathematics a dual topology is a locally convex topology on a dual pair, two vector spaces with a bilinear form defined on them, so that one vector space becomes the continuous dual of the other space.… …   Wikipedia

  • Compact-open topology — In mathematics, the compact open topology is a topology defined on the set of continuous maps between two topological spaces. The compact open topology is one of the commonly used topologies on function spaces, and is applied in homotopy theory… …   Wikipedia

  • Polar topology — In functional analysis and related areas of mathematics a polar topology, topology of mathcal{A} convergence or topology of uniform convergence on the sets of mathcal{A} is a method to define locally convex topologies on the vector spaces of a… …   Wikipedia

  • Convergence of random variables — In probability theory, there exist several different notions of convergence of random variables. The convergence of sequences of random variables to some limit random variable is an important concept in probability theory, and its applications to …   Wikipedia

  • Uniform integrability — The concept of uniform integrability is an important concept in functional analysis and probability theory. If μ is a finite measure, a subset is said to be uniformly integrable if Rephrased with a probabilistic language, the definition… …   Wikipedia

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