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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 more powerful statements (collectively known as transversality theorems) that imply the parametric transversality theorem and are needed for more advanced applications. Informally, the "transversality theorem" states that the set of mappings that are transverse to a given submanifold is a dense open (or, in some cases, only a dense G ...
Transversality may refer to: Transversality (mathematics), a notion in mathematics; Transversality theorem, a theorem in differential topology; See also.
In mathematics, the intersection form of an oriented compact 4-manifold is a special symmetric bilinear form on the 2nd (co)homology group of the 4-manifold. It reflects much of the topology of the 4-manifolds, including information on the existence of a smooth structure.
In mathematics, the Thom space, Thom complex, or Pontryagin–Thom construction (named after René Thom and Lev Pontryagin) of algebraic topology and differential topology is a topological space associated to a vector bundle, over any paracompact space.
The latter is called a transversality condition for a fixed horizon problem. [7] It can be seen that the necessary conditions are identical to the ones stated above for the Hamiltonian. Thus the Hamiltonian can be understood as a device to generate the first-order necessary conditions. [8]
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.
In mathematics, particularly in combinatorics, given a family of sets, here called a collection C, a transversal (also called a cross-section [1] [2] [3]) is a set containing exactly one element from each member of the collection.