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space with two topologies

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  • Space (mathematics) — This article is about mathematical structures called spaces. For space as a geometric concept, see Euclidean space. For all other uses, see space (disambiguation). A hierarchy of mathematical spaces: The inner product induces a norm. The norm… …   Wikipedia

  • Bitopological space — In mathematics, a bitopological space is a set endowed with two topologies. Typically, if the set is X and the topologies are sigma and au then we refer to the bitopological space as (X,sigma, au).Corresponding to properties of topological spaces …   Wikipedia

  • Two-node cluster — A two node cluster is the minimal high availability cluster that can be built.Should one node fail (for a hardware or software problem), the other must acquire the resources being previously managed by the failed node, in order to re enable… …   Wikipedia

  • Topological space — Topological spaces are mathematical structures that allow the formal definition of concepts such as convergence, connectedness, and continuity. They appear in virtually every branch of modern mathematics and are a central unifying notion. The… …   Wikipedia

  • Vector space — This article is about linear (vector) spaces. For the structure in incidence geometry, see Linear space (geometry). Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is… …   Wikipedia

  • Dual space — In mathematics, any vector space, V, has a corresponding dual vector space (or just dual space for short) consisting of all linear functionals on V. Dual vector spaces defined on finite dimensional vector spaces can be used for defining tensors… …   Wikipedia

  • Kolmogorov space — In topology and related branches of mathematics, the T0 spaces or Kolmogorov spaces, named after Andrey Kolmogorov, form a broad class of well behaved topological spaces.The T0 condition is one of the separation axioms. Definition A T0 space is a …   Wikipedia

  • Comparison of topologies — In topology and related areas of mathematics comparison of topologies refers to the fact that two topological structures on a given set may stand in relation to each other. The set of all possible topologies on a given set forms a partially… …   Wikipedia

  • Tychonoff space — Separation Axioms in Topological Spaces Kolmogorov (T0) version T0 | T1 | T2 | T2½ | completely T2 T3 | T3½ | T4 | T5 | T6 In topology and related branches of mathematic …   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

  • Whitney topologies — In mathematics, and especially differential topology, functional analysis and singularity theory, the Whitney topologies are a countably infinite family of topologies defined on the set of smooth mappings between two smooth manifolds. They are… …   Wikipedia

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