# The set of all germs of smooth functions at a point

## Definition

We usually work in the special case of smooth functions, that will be assumed here (so $C^k_p(\mathbb{R}^n)$ is a notation for this set, but there is no general one for other kinds of functions - use words to define them)

• Assume "on $\mathbb{R}^n$" in the absence of a space. That is, assume [ilmath]C^\infty_p[/ilmath] denotes [ilmath]C^\infty_p(\mathbb{R}^n)[/ilmath]

$C^\infty_p(A)$[1][2] is the set of all germs of $C^\infty$ (smooth) functions on [ilmath]A[/ilmath] at [ilmath]p[/ilmath]