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@@ -50,11 +50,13 @@
         (endowed with the Zariski topology) and, for all $U \subseteq V$ open,
         \[
         \mathcal{O}_V(U) \coloneqq
-        \{ f \colon U \to k  \mid  \forall x \in U \exists U_x \subseteq
-        \text{ open neighbourhood of $x$ and polynomials}
-        P, Q \text{ sucht that } \forall z \in U \cap U_x,
+        \left\{ f \colon U \to k\ \middle \vert
+            \begin{array}{l}
+            \forall x \in U \exists x \in U_x \text{ open},
+        P, Q \in k[x_1, \ldots, x_n] \text{ such that }\\ \text{for } z \in U \cap U_x,
         Q(z) \neq 0 \text{ and } f(z) = \frac{P(z)}{Q(z)}
-        \}
+            \end{array}
+        \right\}
         .\] 
     \item $(M, \mathcal{C}^{\infty}_M)$ where
         $M = \varphi^{-1}(0)$ is a non-singular level set of a $\mathcal{C}^{\infty}$