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topological manifold

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  • Topological manifold — In mathematics, a topological manifold is a Hausdorff topological space which looks locally like Euclidean space in a sense defined below. Topological manifolds form an important class of topological spaces with applications throughout… …   Wikipedia

  • Manifold — For other uses, see Manifold (disambiguation). The sphere (surface of a ball) is a two dimensional manifold since it can be represented by a collection of two dimensional maps. In mathematics (specifically in differential geometry and topology),… …   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

  • Topological string theory — In theoretical physics, topological string theory is a simplified version of string theory. The operators in topological string theory represent the algebra of operators in the full string theory that preserve a certain amount of supersymmetry.… …   Wikipedia

  • Topological quantum field theory — A topological quantum field theory (or topological field theory or TQFT) is a quantum field theory which computes topological invariants.Although TQFTs were invented by physicists (notably Edward Witten), they are primarily of mathematical… …   Wikipedia

  • manifold — manifoldly, adv. manifoldness, n. /man euh fohld /, adj. 1. of many kinds; numerous and varied: manifold duties. 2. having numerous different parts, elements, features, forms, etc.: a manifold program for social reform. 3. using, functioning with …   Universalium

  • Topological modular forms — In mathematics, the spectrum of topological modular forms (also known as tmf ) describes a generalized cohomology theory whose coefficient ring is similar to the graded ring of holomorphic modular forms with integral cusp expansions. These rings… …   Wikipedia

  • Topological quantum number — In physics, a topological quantum number is any quantity, in a physical theory, that takes on only one of a discrete set of values, due to topological considerations. Most commonly, topological quantum numbers are topological invariants… …   Wikipedia

  • manifold — I. adjective Etymology: Middle English, from Old English manigfeald, from manig many + feald fold Date: before 12th century 1. a. marked by diversity or variety b. many 2. comprehending or uniting various features ; multifarious 3 …   New Collegiate Dictionary

  • topological space — noun (mathematics) any set of points that satisfy a set of postulates of some kind assume that the topological space is finite dimensional • Syn: ↑mathematical space • Topics: ↑mathematics, ↑math, ↑maths …   Useful english dictionary

  • Differentiable manifold — A nondifferentiable atlas of charts for the globe. The results of calculus may not be compatible between charts if the atlas is not differentiable. In the middle chart the Tropic of Cancer is a smooth curve, whereas in the first it has a sharp… …   Wikipedia

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