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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. It formalizes the idea of a generic intersection in differential topology. It is defined by considering the linearizations of the intersecting spaces at the points of ...
There are several possibilities; see the book by Hirsch. What is usually understood by Thom's transversality theorem is a more powerful statement about jet transversality. See the books by Hirsch and by Golubitsky and Guillemin. The original reference is Thom, Bol. Soc. Mat. Mexicana (2) 1 (1956), pp. 59–71.
Transversality may refer to: Transversality (mathematics), a notion in mathematics; Transversality theorem, a theorem in differential topology; See also
Eisenbud, David; Harris, Joe (2016), 3264 and All That: A Second Course in Algebraic Geometry, Cambridge University Press, ISBN 978-1107602724; Kleiman, Steven L. (1974), "The transversality of a general translate", Compositio Mathematica, 28: 287– 297, MR 0360616
The proof depends on and is intimately related to the transversality properties of smooth manifolds—see Thom transversality theorem. By reversing this construction, John Milnor and Sergei Novikov (among many others) were able to answer questions about the existence and uniqueness of high-dimensional manifolds: this is now known as surgery theory.
In mathematics, the Borsuk–Ulam theorem states that every continuous function from an n-sphere into Euclidean n-space maps some pair of antipodal points to the same point. Here, two points on a sphere are called antipodal if they are in exactly opposite directions from the sphere's center.
Principles of Mathematical Analysis, colloquially known as "PMA" or "Baby Rudin," [1] is an undergraduate real analysis textbook written by Walter Rudin. Initially published by McGraw Hill in 1953, it is one of the most famous mathematics textbooks ever written.
Problem books in mathematics (4 P) Pages in category "Mathematics textbooks" The following 83 pages are in this category, out of 83 total.
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