Support (mathematics)

In mathematics, the carrier (also sometimes support ) usually denotes the closed hull of the " non- zero-set " of a function or other objects.

• 2.1 support a cut
• 2.2 support a sheaf

Analysis

Carrier of a function

The support of is usually referred to.

Be a topological space and a function. The support of then consists of the completed shell of the non- zero set of:

Support of a distribution

Be an open subset of and distribution. It is said that a point of support of a part, and writes, if for every open neighborhood of a function exists with.

If a regular distribution with a constant f, this definition is equivalent to the definition of the support is a function ( the function f).

Support of a Borel measure

The institution of a positive Borel measure on a topological space is the complement of the largest open set with measure 0

Examples

It has, then, because the non- zero set of is their completion is all about. The same applies to any polynomial function other than the function to zero.

It has, if, else, then the amount.

If the characteristic function of if, and if, then the carriers, ie the degree of.

Be an open subset of. The set of all continuous functions with compact support by forming a vector space, which is denoted by.

The set of all smooth ( infinitely often continuously differentiable ) functions with compact support in plays as a set of " test functions " a major role in the theory of distributions.

The delta function has the support, because with true: off If, then.

Sheaf theory

It is a sheaf of abelian groups on a topological space.

Support of a section

For an open subset and a section is called the set of those points for which the image of the stalk is nonzero, the carrier of, usually denoted by or.

The support of a section is always complete.

Support of a sheaf

The carrier itself is the set of points for which the stalk is not zero.

The support of a sheaf is not necessarily complete, the support of a coherent sheaf module does.