Definition:Space of Smooth Real Functions

Definition

Let $M$ be a smooth manifold with or without boundary.

The set of all smooth real functions is called the space of smooth real functions and is denoted $\map {\mathrm C^\infty} {M, \R}$, often simplified to $\map {\mathrm C^\infty} M$.

Also see

• Results about smooth real functions can be found here.

Sources

• 1971: Frank W. Warner: Foundations of differentiable manifolds and Lie groups: Chapter $1$: Manifolds: $\S$ Differentiable Manifolds