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A function with k continuous derivatives is called a C^k function. In order to specify a C^k function on a domain X, the notation C^k(X) is used. The most common C^k space is ...

The delta function is a generalized function that can be defined as the limit of a class of delta sequences. The delta function is sometimes called "Dirac's delta function" ...

A smooth manifold with a Poisson bracket defined on its function space.

Topological lower bounds in terms of Betti numbers for the number of critical points form a smooth function on a smooth manifold.

The singular support of a generalized function u is the complement of the largest open set on which u is smooth. Roughly speaking, it is the closed set where the distribution ...

The class of all regular sequences of particularly well-behaved functions equivalent to a given regular sequence. A distribution is sometimes also called a "generalized ...

The Heaviside step function is a mathematical function denoted H(x), or sometimes theta(x) or u(x) (Abramowitz and Stegun 1972, p. 1020), and also known as the "unit step ...

An anchor is the bundle map rho from a vector bundle A to the tangent bundle TB satisfying 1. [rho(X),rho(Y)]=rho([X,Y]) and 2. [X,phiY]=phi[X,Y]+(rho(X)·phi)Y, where X and Y ...

A symplectic form on a smooth manifold M is a smooth closed 2-form omega on M which is nondegenerate such that at every point m, the alternating bilinear form omega_m on the ...

A partial function is a function that is not total.