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rav lec: fix formatting

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Christian Merten 3 anos atrás
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f5a077e53f
Acessado por: christian <christian@flavigny.de> ID da chave GPG: D953D69721B948B3
3 arquivos alterados com 6 adições e 4 exclusões
  1. BIN
      ws2022/rav/lecture/rav.pdf
  2. BIN
      ws2022/rav/lecture/rav5.pdf
  3. +6
    -4
      ws2022/rav/lecture/rav5.tex

BIN
ws2022/rav/lecture/rav.pdf Ver arquivo


BIN
ws2022/rav/lecture/rav5.pdf Ver arquivo


+ 6
- 4
ws2022/rav/lecture/rav5.tex Ver arquivo

@@ -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 $\mathcal{C}^{\infty}$


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