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 [math]C^k_p(\mathbb{R}^n)[/math] is a notation for this set, but there is no general one for other kinds of functions - use words to define them)

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

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

See also

• Germ
• Tangent space