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 $C^\infty_p$ denotes $C^\infty_p(\mathbb{R}^n)$

$$C^\infty_p(A)$$ is the set of all germs of $$C^\infty$$ (smooth) functions on $A$ at $p$

See also

• Germ
• Tangent space