Editing Generalized function (section)

===Sheaf structure===

If (''E'',''P'') is a (pre-)[[sheaf (mathematics)|sheaf]] of semi normed algebras on some topological space ''X'', then ''G<sub>s</sub>''(''E'',&nbsp;''P'') will also have this property. This means that the notion of [[Restriction (mathematics)|restriction]] will be defined, which allows to define the [[support (mathematics)|support]] of a generalized function w.r.t. a subsheaf, in particular:
* For the subsheaf {0}, one gets the usual support (complement of the largest open subset where the function is zero).
* For the subsheaf ''E'' (embedded using the canonical (constant) injection), one gets what is called the [[singular support]], i.e., roughly speaking, the closure of the set where the generalized function is not a smooth function (for ''E''&nbsp;=&nbsp;''C''<sup>∞</sup>).