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\coloneqq - \{ f \colon U \to k \mid \forall x \in U \exists U_x \subseteq - \text{ open neighbourhood of $x$ and polynomials} - P, Q \text{ sucht that } \forall z \in U \cap U_x, + \left\{ f \colon U \to k\ \middle \vert + \begin{array}{l} + \forall x \in U \exists x \in U_x \text{ open}, + P, Q \in k[x_1, \ldots, x_n] \text{ such that }\\ \text{for } z \in U \cap U_x, Q(z) \neq 0 \text{ and } f(z) = \frac{P(z)}{Q(z)} - \} + \end{array} + \right\} .\] \item $(M, \mathcal{C}^{\infty}_M)$ where $M = \varphi^{-1}(0)$ is a non-singular level set of a $\mathcal{C}^{\infty}$