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40 relations: André Haefliger, C. T. C. Wall, Characteristic class, Circle, Differentiable manifold, Differential topology, Dimension, Embedding, H-cobordism, Hassler Whitney, Hausdorff space, History of manifolds and varieties, Homotopy, Immersion (mathematics), John Milnor, Klein bottle, Manifold, Mathematics, Morris Hirsch, N-connected space, N-sphere, Nash embedding theorem, Poincaré conjecture, Power of two, Real coordinate space, Real number, Real projective space, Representation theorem, Second-countable space, Sergei Novikov (mathematician), Simon Donaldson, Simply connected space, Smooth structure, Smoothness, Stephen Smale, Surgery theory, Transversality (mathematics), Vladimir Abramovich Rokhlin, Whitney immersion theorem, William S. Massey.
André Haefliger
André Haefliger (born 22 May 1929) is a Swiss mathematician who works primarily on topology.
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C. T. C. Wall
Charles Terence Clegg "Terry" Wall (born 14 December 1936) is a British mathematician, educated at Marlborough and Trinity College, Cambridge.
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Characteristic class
In mathematics, a characteristic class is a way of associating to each principal bundle X a cohomology class of X. The cohomology class measures the extent the bundle is "twisted" — and whether it possesses sections.
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Circle
A circle is a simple closed shape.
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Differentiable manifold
In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a linear space to allow one to do calculus.
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Differential topology
In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds.
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Dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.
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Embedding
In mathematics, an embedding (or imbedding) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup.
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H-cobordism
In geometric topology and differential topology, an (n + 1)-dimensional cobordism W between n-dimensional manifolds M and N is an h-cobordism (the h stands for homotopy equivalence) if the inclusion maps are homotopy equivalences.
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Hassler Whitney
Hassler Whitney (March 23, 1907 – May 10, 1989) was an American mathematician.
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Hausdorff space
In topology and related branches of mathematics, a Hausdorff space, separated space or T2 space is a topological space in which distinct points have disjoint neighbourhoods.
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History of manifolds and varieties
The study of manifolds combines many important areas of mathematics: it generalizes concepts such as curves and surfaces as well as ideas from linear algebra and topology.
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Homotopy
In topology, two continuous functions from one topological space to another are called homotopic (from Greek ὁμός homós "same, similar" and τόπος tópos "place") if one can be "continuously deformed" into the other, such a deformation being called a homotopy between the two functions.
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Immersion (mathematics)
In mathematics, an immersion is a differentiable function between differentiable manifolds whose derivative is everywhere injective.
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John Milnor
John Willard Milnor (born February 20, 1931) is an American mathematician known for his work in differential topology, K-theory and dynamical systems.
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Klein bottle
In topology, a branch of mathematics, the Klein bottle is an example of a non-orientable surface; it is a two-dimensional manifold against which a system for determining a normal vector cannot be consistently defined.
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Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Morris Hirsch
Morris William Hirsch (born June 28, 1933) is an American mathematician, formerly at the University of California, Berkeley.
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N-connected space
In the mathematical branch of algebraic topology, specifically homotopy theory, n-connectedness (sometimes, n-simple connectedness) generalizes the concepts of path-connectedness and simple connectedness.
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N-sphere
In mathematics, the n-sphere is the generalization of the ordinary sphere to spaces of arbitrary dimension.
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Nash embedding theorem
The Nash embedding theorems (or imbedding theorems), named after John Forbes Nash, state that every Riemannian manifold can be isometrically embedded into some Euclidean space.
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Poincaré conjecture
In mathematics, the Poincaré conjecture is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space.
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Power of two
In mathematics, a power of two is a number of the form where is an integer, i.e. the result of exponentiation with number two as the base and integer as the exponent.
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Real coordinate space
In mathematics, real coordinate space of dimensions, written R (also written with blackboard bold) is a coordinate space that allows several (''n'') real variables to be treated as a single variable.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Real projective space
In mathematics, real projective space, or RPn or \mathbb_n(\mathbb), is the topological space of lines passing through the origin 0 in Rn+1.
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Representation theorem
In mathematics, a representation theorem is a theorem that states that every abstract structure with certain properties is isomorphic to another (abstract or concrete) structure.
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Second-countable space
In topology, a second-countable space, also called a completely separable space, is a topological space whose topology has a countable base.
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Sergei Novikov (mathematician)
Sergei Petrovich Novikov (also Serguei) (Russian: Серге́й Петро́вич Но́виков) (born 20 March 1938) is a Soviet and Russian mathematician, noted for work in both algebraic topology and soliton theory.
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Simon Donaldson
Sir Simon Kirwan Donaldson FRS (born 20 August 1957), is an English mathematician known for his work on the topology of smooth (differentiable) four-dimensional manifolds and Donaldson–Thomas theory.
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Simply connected space
In topology, a topological space is called simply connected (or 1-connected, or 1-simply connected) if it is path-connected and every path between two points can be continuously transformed (intuitively for embedded spaces, staying within the space) into any other such path while preserving the two endpoints in question.
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Smooth structure
In mathematics, a smooth structure on a manifold allows for an unambiguous notion of smooth function.
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Smoothness
In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.
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Stephen Smale
Stephen Smale (born July 15, 1930) is an American mathematician from Flint, Michigan.
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Surgery theory
In mathematics, specifically in geometric topology, surgery theory is a collection of techniques used to produce one finite-dimensional manifold from another in a 'controlled' way, introduced by.
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Transversality (mathematics)
In mathematics, transversality is a notion that describes how spaces can intersect; transversality can be seen as the "opposite" of tangency, and plays a role in general position.
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Vladimir Abramovich Rokhlin
Vladimir Abramovich Rokhlin (Russian: Влади́мир Абра́мович Ро́хлин) (23 August 1919 – 3 December 1984) was a Soviet mathematician, who made numerous contributions in algebraic topology, geometry, measure theory, probability theory, ergodic theory and entropy theory.
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Whitney immersion theorem
In differential topology, the Whitney immersion theorem states that for m>1, any smooth m-dimensional manifold (required also to be Hausdorff and second-countable) has a one-to-one immersion in Euclidean 2m-space, and a (not necessarily one-to-one) immersion in (2m-1)-space.
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William S. Massey
William Schumacher Massey (August 23, 1920 - June 17, 2017) was an American mathematician, known for his work in algebraic topology.
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Whitney Embedding Theorem, Whitney Trick, Whitney trick, Whitney's Theorem, Whitney's embedding theorem.
References
[1] https://en.wikipedia.org/wiki/Whitney_embedding_theorem
