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  1. en.wikipedia.org › wiki › Hausdorff_spaceHausdorff space - Wikipedia

    In topology and related branches of mathematics, a Hausdorff space (/ ˈ h aʊ s d ɔːr f / HOWSS-dorf, / ˈ h aʊ z d ɔːr f / HOWZ-dorf), separated space or T 2 space is a topological space where, for any two distinct points, there exist neighbourhoods of each that are disjoint from each other.

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    • Hausdorff Example 1: Cofinite Topology - YouTube
    • 1: Gromov-Hausdorff space: general properties. | Download Scientific ...
    • Topology| Lec 21 - 6.2: Hausdorff Spaces - YouTube
    • Topology Lecture 07: Hausdorff Spaces - YouTube

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  3. de.wikipedia.org › wiki › Hausdorff-RaumHausdorff-Raum – Wikipedia

    Zwei Punkte, die durch Umgebungen getrennt werden. Ein Hausdorff-Raum (auch hausdorffscher Raum oder Hausdorffraum; nach Felix Hausdorff) oder separierter Raum ist ein topologischer Raum , in dem das Trennungsaxiom (auch Hausdorffeigenschaft oder hausdorffsches Trennungsaxiom genannt) gilt.

  4. maths.qmul.ac.uk › ~bill › topchapter33. Hausdorff Spaces and Compact Spaces 3.1 Hausdorff Spaces

    topology and U,V are nonempty, C X(U) and C X(V) are finite. But then X = C X(∅) = C X (U T V) = C X (U) S C X (V ) is finite - contradiction. (3.1b) Let X be a Hausdorff space and let Z ⊂ X. Then Z (regarded as a topological space via the subspace topology) is Hausdorff. Proof Let x,y ∈ Z. Since X is Hausdorff there exist open sets ...

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  6. mathworld.wolfram.com › HausdorffTopologyHausdorff Topology -- from Wolfram MathWorld

    16. Mai 2024 · TOPICS. Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory Probability and Statistics Recreational Mathematics Topology Alphabetical Index New in MathWorld

  7. www.britannica.com › science › Hausdorff-spaceHausdorff space | Topology, Metric Spaces & Compactness

    Hausdorff space, in mathematics, type of topological space named for the German mathematician Felix Hausdorff. A topological space is a generalization of the notion of an object in three-dimensional space. It consists of an abstract set of points along with a specified collection of subsets, called.

  8. www.mathematics.uni-bonn.de › hcmHausdorff Center for Mathematics — HCM - uni-bonn.de

    18. Apr. 2024 · With his masterpiece Grundzüge der Mengenlehre (1914), Hausdorff established topology as an independent discipline in mathematics. In addition, Hausdorff made significant contributions to general and descriptive set theory, measure theory, algebra, functional anaylsis, probability theory, and insurance mathematics.

  9. ncatlab.org › nlab › showHausdorff space in nLab

    30. Juni 2023 · Hausdorff space in nLab. Home Page | All Pages | Latest Revisions | Discuss this page |. Context. Topology. Contents. 1. Idea. 2. Definitions. 3. Examples. 4. Properties. 5. In terms of lifting properties. 6. Hausdorff reflection. 7. Monadicity. 8. Sobriety. 9. Relation to compact spaces. 10. Dense subspaces and Epimorphisms. 11. Related notions.