determined by the linear space ${\mathcal{F}}(M)$, in the sense that points of $M$ are in one-to-one correspondence with a particular class of linear functionals on ${\mathcal{F}}(M)$, to wit, multiplicative ones. One writes $\<x,h>:=h(x)$ to express this correspondence. As a consequence $M{\hookrightarrow}{\mathcal{F}}'(M)$, where ${\mathcal{F}}'(M)$ is the space of compactly supported distributions on $M$. We denote by ${\mathbb{C}}M$ the subspace of ${\mathcal{F}}'(M)$ generated by the points of $M$. It will sometimes be convenient to write $Th=\<T,h>$ for the value of the distribution $T\in{\mathcal{F}}'(M)$ at $h\in{\mathcal{F}}(M)$; accordingly we abbreviate to $xh=h(x)$. Many other geometrical objects can be expressed as functionals in this way; for instance, if $v_x\in T_xM$, then $\<v_x,h>\equiv v_xh$ is the derivative of $h$ in the direction of the tangent vector $v_x$ at $x$. Therefore $TM{\hookrightarrow}{\mathcal{F}}'(M)$, too. If $X$ is a smooth vector field and $Xh:=X(h)$, then $xX$ is defined naturally by $$(xX)h = x(Xh).$$ That is, $xX=X(x)$; and we may omit the parentheses in $xXh$. An advantage of thinking in this way is that operations in principle not meaningful on $M$ make sense in ${\mathcal{F}}'(M)$. For instance, given a curve ${\gamma}:{\mathbb{R}}_t\to M$ with ${\gamma}(0)=x_0$, the definition $$\dot{\gamma}(0) = \lim_{{\varepsilon}\downarrow0}\frac{{\gamma}({\varepsilon}) - x_0}{{\varepsilon}},$$ which looks unacceptable on $M$, in ${\mathcal{F}}'(M)$ just means 