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Given a vector bundle pi:E->M, its dual bundle is a vector bundle pi^*:E^*->M. The fiber bundle of E^* over a point p in M is the dual vector space to the fiber of E.

A sequence {a_1,a_2,a_3,...} fulfils a given property eventually if it fulfils it from some point onward, or, more precisely, if the property is fulfilled by the subsequence ...

Fatou dust is a Fatou set for a point outside the underlying set. Such a set has zero area and has an infinite number of disconnected components.

The abscissas of the N-point Gaussian quadrature formula are precisely the roots of the orthogonal polynomial for the same interval and weighting function.

If P is any point on a line TT^' whose orthopole is S, then the circle power of S with respect to the pedal circle of P is a constant (Gallatly 1913, p. 51).

A linear approximation to a function f(x) at a point x_0 can be computed by taking the first term in the Taylor series f(x_0+Deltax)=f(x_0)+f^'(x_0)Deltax+....

The lengths of the tangents from a point P to a conic C are proportional to the cube roots of the radii of curvature of C at the corresponding points of contact.

A function for which several distinct functional values correspond (as a result of different continuations) to one and the same point (Knopp 1996, p. 94).

A base for a neighborhood system of a point x is a collection N of open sets such that x belongs to every member of N, and any open set containing x also contains a member of ...

The y- (vertical) coordinate of a point in a two dimensional coordinate system. Physicists and astronomers sometimes use the term to refer to the axis itself instead of the ...