2 problems

For a smooth manifold $M$, let … be the set of almost invertible smooth functions. Since $S$ contains $1$, is closed under multiplication, and contains no zero divisors, define the…

For a smooth manifold $M$, let $C^\infty_d(M)$ be the $\mathbb{R}$-algebra of densely defined smooth functions $f:(D_f\subseteq M)\to\mathbb{R}$, where each domain $D_f$ is an embe…