From c34b47089a133e58032fe4ea52f61efacaf5f548 Mon Sep 17 00:00:00 2001
From: Juan Marin Noguera <juan@mnpi.eu>
Date: Sun, 4 Dec 2022 22:49:17 +0100
Subject: Oops

---
 fvc/n2.lyx | 44 ++++++++++++++++++++++----------------------
 fvc/n3.lyx | 10 +++++-----
 fvc/n4.lyx | 50 +++++++++++++++++++++++++-------------------------
 3 files changed, 52 insertions(+), 52 deletions(-)

(limited to 'fvc')

diff --git a/fvc/n2.lyx b/fvc/n2.lyx
index 61c71c9..55f969a 100644
--- a/fvc/n2.lyx
+++ b/fvc/n2.lyx
@@ -91,7 +91,7 @@ Teorema de Cauchy-Goursat:
 \end_inset
 
  y 
-\begin_inset Formula $\Delta(a,b,c):=\{\mu a+\lambda b+\gamma c\mid \mu+\lambda+\gamma=1;\mu,\lambda,\gamma\geq0\}\subseteq\Omega$
+\begin_inset Formula $\Delta(a,b,c)\coloneqq \{\mu a+\lambda b+\gamma c\mid \mu+\lambda+\gamma=1;\mu,\lambda,\gamma\geq0\}\subseteq\Omega$
 \end_inset
 
 , entonces
@@ -111,23 +111,23 @@ Teorema de Cauchy-Goursat:
 Demostración:
 \series default
  Sean 
-\begin_inset Formula $\gamma:=[a,b,c,a]$
+\begin_inset Formula $\gamma\coloneqq [a,b,c,a]$
 \end_inset
 
 , 
-\begin_inset Formula $\Delta:=\Delta(a,b,c)$
+\begin_inset Formula $\Delta\coloneqq \Delta(a,b,c)$
 \end_inset
 
 , 
-\begin_inset Formula $a':=\frac{b+c}{2}$
+\begin_inset Formula $a'\coloneqq \frac{b+c}{2}$
 \end_inset
 
 , 
-\begin_inset Formula $b':=\frac{a+c}{2}$
+\begin_inset Formula $b'\coloneqq \frac{a+c}{2}$
 \end_inset
 
 , 
-\begin_inset Formula $c':=\frac{a+b}{2}$
+\begin_inset Formula $c'\coloneqq \frac{a+b}{2}$
 \end_inset
 
  e
@@ -156,7 +156,7 @@ Sean
 
 \begin_layout Itemize
 Si 
-\begin_inset Formula $|J_{k}|:=\max_{i}|J_{i}|$
+\begin_inset Formula $|J_{k}|\coloneqq \max_{i}|J_{i}|$
 \end_inset
 
 , 
@@ -206,7 +206,7 @@ Para
 \end_inset
 
 , 
-\begin_inset Formula $F(x):=\frac{x+a}{2}$
+\begin_inset Formula $F(x)\coloneqq \frac{x+a}{2}$
 \end_inset
 
  es una biyección de 
@@ -218,11 +218,11 @@ Para
 \end_inset
 
 , pues si 
-\begin_inset Formula $x:=ra+sb+tc$
+\begin_inset Formula $x\coloneqq ra+sb+tc$
 \end_inset
 
 , 
-\begin_inset Formula $F(x):=\frac{ra+sb+tc+a}{2}=\frac{ra+sb+tc+(r+s+t)a}{2}=ra+s\frac{a+b}{2}+t\frac{a+c}{2}=ra+sc'+tb'$
+\begin_inset Formula $F(x)\coloneqq \frac{ra+sb+tc+a}{2}=\frac{ra+sb+tc+(r+s+t)a}{2}=ra+s\frac{a+b}{2}+t\frac{a+c}{2}=ra+sc'+tb'$
 \end_inset
 
 .
@@ -236,7 +236,7 @@ Para
 \end_inset
 
  la biyección 
-\begin_inset Formula $F(x):=\frac{a+b+c-x}{2}$
+\begin_inset Formula $F(x)\coloneqq \frac{a+b+c-x}{2}$
 \end_inset
 
 .
@@ -245,11 +245,11 @@ Para
 \end_deeper
 \begin_layout Standard
 Sean entonces 
-\begin_inset Formula $I_{1}:=\max_{i}|J_{i}|$
+\begin_inset Formula $I_{1}\coloneqq \max_{i}|J_{i}|$
 \end_inset
 
 , 
-\begin_inset Formula $\gamma_{1}:=[a_{1},b_{1},c_{1},a_{1}]$
+\begin_inset Formula $\gamma_{1}\coloneqq [a_{1},b_{1},c_{1},a_{1}]$
 \end_inset
 
  la curva correspondiente a 
@@ -257,7 +257,7 @@ Sean entonces
 \end_inset
 
  y 
-\begin_inset Formula $\Delta_{1}:=\Delta(a_{1},b_{1},c_{1})$
+\begin_inset Formula $\Delta_{1}\coloneqq \Delta(a_{1},b_{1},c_{1})$
 \end_inset
 
 , con lo que 
@@ -297,7 +297,7 @@ Sean entonces
 
 .
  Sea 
-\begin_inset Formula $p(z):=f(\alpha)+f'(\alpha)(z-\alpha)$
+\begin_inset Formula $p(z)\coloneqq f(\alpha)+f'(\alpha)(z-\alpha)$
 \end_inset
 
  una función polinómica y por tanto con primitiva, entonces
@@ -539,11 +539,11 @@ Si
 \end_inset
 
 , sean 
-\begin_inset Formula $c_{\rho}:=(1-\rho)a+\rho b$
+\begin_inset Formula $c_{\rho}\coloneqq (1-\rho)a+\rho b$
 \end_inset
 
  y 
-\begin_inset Formula $b_{\rho}:=(1-\rho)a+\rho c$
+\begin_inset Formula $b_{\rho}\coloneqq (1-\rho)a+\rho c$
 \end_inset
 
  para 
@@ -1221,7 +1221,7 @@ Demostración:
 
 .
  Sea 
-\begin_inset Formula $f(z):=\frac{1}{p(z)}$
+\begin_inset Formula $f(z)\coloneqq \frac{1}{p(z)}$
 \end_inset
 
 , 
@@ -1279,7 +1279,7 @@ Demostración:
 
 .
  Sea entonces 
-\begin_inset Formula $g(z):=\frac{1}{f(z)-\alpha}$
+\begin_inset Formula $g(z)\coloneqq \frac{1}{f(z)-\alpha}$
 \end_inset
 
  una función entera, como 
@@ -1393,7 +1393,7 @@ luego
 \end_inset
 
 , por el teorema de Taylor, sea 
-\begin_inset Formula $c_{n}:=\frac{F^{(n)}(\alpha)}{n!}$
+\begin_inset Formula $c_{n}\coloneqq \frac{F^{(n)}(\alpha)}{n!}$
 \end_inset
 
 , como 
@@ -1473,7 +1473,7 @@ Teorema de convergencia de Weierstrass:
 \end_inset
 
  y 
-\begin_inset Formula $f(z):=\lim_{n}f_{n}(z)$
+\begin_inset Formula $f(z)\coloneqq \lim_{n}f_{n}(z)$
 \end_inset
 
  para 
@@ -1583,7 +1583,7 @@ Sean
 \end_inset
 
  y 
-\begin_inset Formula $H:=\{z\in\mathbb{C}\mid d(z,K)\leq\rho\}$
+\begin_inset Formula $H\coloneqq \{z\in\mathbb{C}\mid d(z,K)\leq\rho\}$
 \end_inset
 
 , con lo que 
diff --git a/fvc/n3.lyx b/fvc/n3.lyx
index a2494f8..1e9215c 100644
--- a/fvc/n3.lyx
+++ b/fvc/n3.lyx
@@ -87,7 +87,7 @@ Sean
 \end_inset
 
  y 
-\begin_inset Formula $Z(f):=\{z\in\Omega\mid f(z)=0\}$
+\begin_inset Formula $Z(f)\coloneqq \{z\in\Omega\mid f(z)=0\}$
 \end_inset
 
 , 
@@ -139,7 +139,7 @@ f(z)=\sum_{n=0}^{\infty}c_{n}(z-a)^{n}
 \end_inset
 
 para 
-\begin_inset Formula $c_{n}:=\frac{f^{(n)}(a)}{n!}$
+\begin_inset Formula $c_{n}\coloneqq \frac{f^{(n)}(a)}{n!}$
 \end_inset
 
 , y queremos ver que todos los 
@@ -169,7 +169,7 @@ para
 \end_inset
 
 Sea 
-\begin_inset Formula $g_{k}(z):=\sum_{n=k+1}^{\infty}c_{n}(z-a)^{n-k}$
+\begin_inset Formula $g_{k}(z)\coloneqq \sum_{n=k+1}^{\infty}c_{n}(z-a)^{n-k}$
 \end_inset
 
  una función holomorfa en 
@@ -210,7 +210,7 @@ status open
 \end_inset
 
  Sea 
-\begin_inset Formula $A:=\{z\in\Omega\mid \forall k\in\mathbb{N},f^{(k)}(z)=0\}\neq\emptyset$
+\begin_inset Formula $A\coloneqq \{z\in\Omega\mid \forall k\in\mathbb{N},f^{(k)}(z)=0\}\neq\emptyset$
 \end_inset
 
 , pues 
@@ -337,7 +337,7 @@ principio de identidad para funciones holomorfas
 \end_inset
 
  no es idénticamente nula, entonces todo punto de 
-\begin_inset Formula $Z(f):=\{z\in\Omega\mid f(z)=0\}$
+\begin_inset Formula $Z(f)\coloneqq \{z\in\Omega\mid f(z)=0\}$
 \end_inset
 
  es aislado y 
diff --git a/fvc/n4.lyx b/fvc/n4.lyx
index cfd60f7..8feaa83 100644
--- a/fvc/n4.lyx
+++ b/fvc/n4.lyx
@@ -108,7 +108,7 @@ Toda curva
 Demostración:
 \series default
  Sean 
-\begin_inset Formula $\rho:=\min_{t\in[a,b]}|\gamma(t)|>0$
+\begin_inset Formula $\rho\coloneqq \min_{t\in[a,b]}|\gamma(t)|>0$
 \end_inset
 
 , 
@@ -140,7 +140,7 @@ Demostración:
 \end_inset
 
  y 
-\begin_inset Formula $D_{k}:=D(\gamma(t_{k}),\rho)$
+\begin_inset Formula $D_{k}\coloneqq D(\gamma(t_{k}),\rho)$
 \end_inset
 
 .
@@ -180,11 +180,11 @@ Demostración:
 
 .
  Sean ahora 
-\begin_inset Formula $\theta_{k}(t):=A_{k}(\gamma(t))\in\text{Arg}(\gamma(t))$
+\begin_inset Formula $\theta_{k}(t)\coloneqq A_{k}(\gamma(t))\in\text{Arg}(\gamma(t))$
 \end_inset
 
  y 
-\begin_inset Formula $m_{k}:=\theta_{k}(t_{k})-\theta_{k+1}(t_{k})$
+\begin_inset Formula $m_{k}\coloneqq \theta_{k}(t_{k})-\theta_{k+1}(t_{k})$
 \end_inset
 
 , y definimos 
@@ -192,7 +192,7 @@ Demostración:
 \end_inset
 
  como 
-\begin_inset Formula $\theta(t):=\theta_{k}(t)+\sum_{i=0}^{k-1}m_{k}$
+\begin_inset Formula $\theta(t)\coloneqq \theta_{k}(t)+\sum_{i=0}^{k-1}m_{k}$
 \end_inset
 
  para 
@@ -334,7 +334,7 @@ Sean
 \end_inset
 
 , 
-\begin_inset Formula $\rho:=\min_{t\in[a,b]}|\gamma(t)-z_{0}|>0$
+\begin_inset Formula $\rho\coloneqq \min_{t\in[a,b]}|\gamma(t)-z_{0}|>0$
 \end_inset
 
  y 
@@ -371,7 +371,7 @@ Sean
 \end_inset
 
 , tenemos que 
-\begin_inset Formula $\theta(t):=\theta_{0}(t)+\arg\frac{\gamma(t)-z}{\gamma(t)-z_{0}}$
+\begin_inset Formula $\theta(t)\coloneqq \theta_{0}(t)+\arg\frac{\gamma(t)-z}{\gamma(t)-z_{0}}$
 \end_inset
 
  es un argumento continuo de 
@@ -499,7 +499,7 @@ Demostración:
 \end_inset
 
 , entonces 
-\begin_inset Formula $\varphi(t):=\log|\gamma(t)-z|+i\theta(t)$
+\begin_inset Formula $\varphi(t)\coloneqq \log|\gamma(t)-z|+i\theta(t)$
 \end_inset
 
  es un logaritmo continuo de 
@@ -525,7 +525,7 @@ Demostración:
 
  es derivable.
  Entonces 
-\begin_inset Formula $\varphi_{k}:=\varphi|_{[t_{k-1},t_{k}]}$
+\begin_inset Formula $\varphi_{k}\coloneqq \varphi|_{[t_{k-1},t_{k}]}$
 \end_inset
 
  también lo es y 
@@ -560,7 +560,7 @@ Una
 cadena
 \series default
  es una expresión de la forma 
-\begin_inset Formula $\Gamma:=m_{1}\gamma_{1}+\dots+m_{q}\gamma_{q}$
+\begin_inset Formula $\Gamma\coloneqq m_{1}\gamma_{1}+\dots+m_{q}\gamma_{q}$
 \end_inset
 
  donde los 
@@ -581,7 +581,7 @@ soporte
 \end_inset
 
  a 
-\begin_inset Formula $\Gamma^{*}:=\bigcup_{k}\gamma_{k}^{*}$
+\begin_inset Formula $\Gamma^{*}\coloneqq \bigcup_{k}\gamma_{k}^{*}$
 \end_inset
 
  y 
@@ -593,16 +593,16 @@ longitud
 \end_inset
 
  a 
-\begin_inset Formula $\ell(\Gamma):=\sum_{k}|m_{k}|\ell(\gamma_{k})$
+\begin_inset Formula $\ell(\Gamma)\coloneqq \sum_{k}|m_{k}|\ell(\gamma_{k})$
 \end_inset
 
 .
  Si 
-\begin_inset Formula $\Sigma:=n_{1}\sigma_{1}+\dots+n_{p}\sigma_{p}$
+\begin_inset Formula $\Sigma\coloneqq n_{1}\sigma_{1}+\dots+n_{p}\sigma_{p}$
 \end_inset
 
  es otra cadena, llamamos 
-\begin_inset Formula $\Gamma+\Sigma:=m_{1}\gamma_{1}+\dots+m_{q}\gamma_{q}+k_{1}\sigma_{1}+\dots+k_{p}\sigma_{p}$
+\begin_inset Formula $\Gamma+\Sigma\coloneqq m_{1}\gamma_{1}+\dots+m_{q}\gamma_{q}+k_{1}\sigma_{1}+\dots+k_{p}\sigma_{p}$
 \end_inset
 
 .
@@ -647,7 +647,7 @@ ciclo
 \end_inset
 
  a 
-\begin_inset Formula $\text{Ind}_{\Gamma}(z):=\sum_{k}m_{k}\text{Ind}_{\gamma_{k}}(z)$
+\begin_inset Formula $\text{Ind}_{\Gamma}(z)\coloneqq \sum_{k}m_{k}\text{Ind}_{\gamma_{k}}(z)$
 \end_inset
 
 .
@@ -806,7 +806,7 @@ es continua en
 \end_inset
 
 Como 
-\begin_inset Formula $K:=\{\{z_{n}\}_{n}\cup\{a\}\}\times\Gamma^{*}$
+\begin_inset Formula $K\coloneqq \{\{z_{n}\}_{n}\cup\{a\}\}\times\Gamma^{*}$
 \end_inset
 
  es compacto por ser producto de compactos, 
@@ -889,7 +889,7 @@ Si además, para
 \end_inset
 
  dada por 
-\begin_inset Formula $F_{w}(z):=F(z,w)$
+\begin_inset Formula $F_{w}(z)\coloneqq F(z,w)$
 \end_inset
 
  es holomorfa en 
@@ -1059,7 +1059,7 @@ Ahora bien, fijado
 \end_inset
 
 , sea 
-\begin_inset Formula $F_{w}(z):=F(w,z)$
+\begin_inset Formula $F_{w}(z)\coloneqq F(w,z)$
 \end_inset
 
 , es claro que 
@@ -1083,7 +1083,7 @@ Ahora bien, fijado
 
 \begin_layout Standard
 Sea 
-\begin_inset Formula $\Omega_{0}:=\{z\in\mathbb{C}\setminus\Gamma^{*}\mid \text{Ind}_{\Gamma}(z)=0\}$
+\begin_inset Formula $\Omega_{0}\coloneqq \{z\in\mathbb{C}\setminus\Gamma^{*}\mid \text{Ind}_{\Gamma}(z)=0\}$
 \end_inset
 
 , que es abierto por ser unión de componentes conexas de 
@@ -1123,7 +1123,7 @@ status open
 \end_inset
 
  dada por 
-\begin_inset Formula $F_{0}(z,w):=\frac{f(w)}{w-z}$
+\begin_inset Formula $F_{0}(z,w)\coloneqq \frac{f(w)}{w-z}$
 \end_inset
 
 .
@@ -1302,7 +1302,7 @@ forma general del teorema de Cauchy
 \end_inset
 
 , aplicando la fórmula integral de Cauchy a 
-\begin_inset Formula $g(z):=(z-a)f(z)$
+\begin_inset Formula $g(z)\coloneqq (z-a)f(z)$
 \end_inset
 
 , como 
@@ -1886,7 +1886,7 @@ status open
 
 .
  Sea 
-\begin_inset Formula $K:=\mathbb{C}\setminus\Omega_{0}=\Gamma^{*}\cup\{z\in\mathbb{C}\setminus\Gamma^{*}\mid \text{Ind}_{\Gamma}(z)\neq0\}$
+\begin_inset Formula $K\coloneqq \mathbb{C}\setminus\Omega_{0}=\Gamma^{*}\cup\{z\in\mathbb{C}\setminus\Gamma^{*}\mid \text{Ind}_{\Gamma}(z)\neq0\}$
 \end_inset
 
 , que es cerrado por ser complementario de un abierto y acotado porque no
@@ -1934,15 +1934,15 @@ Sean
 \end_inset
 
 , 
-\begin_inset Formula $m_{k}:=\text{Ind}_{\Gamma}(a_{k})$
+\begin_inset Formula $m_{k}\coloneqq \text{Ind}_{\Gamma}(a_{k})$
 \end_inset
 
 , 
-\begin_inset Formula $\gamma_{k}:=C(a_{k},\rho)$
+\begin_inset Formula $\gamma_{k}\coloneqq C(a_{k},\rho)$
 \end_inset
 
  y 
-\begin_inset Formula $\Sigma:=\sum_{k=1}^{q}m_{k}\gamma_{k}$
+\begin_inset Formula $\Sigma\coloneqq \sum_{k=1}^{q}m_{k}\gamma_{k}$
 \end_inset
 
 .
-- 
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