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presheaf_._topology [2014/10/30 10:25] nikolaj |
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| A [[sheaf]] $F$ is particular kind of contravariant functor which helps to capture sections. The object image of a sheaf of a an open set $FU$ is a local function space. | A [[sheaf]] $F$ is particular kind of contravariant functor which helps to capture sections. The object image of a sheaf of a an open set $FU$ is a local function space. | ||
| - | === Example === | + | === Examples === |
| * Consider the sheaf $C^\infty$ of all smooth functions over $X$. If $U$ is an open set of $X$, then the objects $C^\infty U:=\{f:U\to\mathbb R\ |\ f\dots\text{smooth} \}$ is the restriction of such functions to $U$. | * Consider the sheaf $C^\infty$ of all smooth functions over $X$. If $U$ is an open set of $X$, then the objects $C^\infty U:=\{f:U\to\mathbb R\ |\ f\dots\text{smooth} \}$ is the restriction of such functions to $U$. | ||
