Oops

1 files changed, 35 insertions, 35 deletions

diff --git a/ts/n3.lyx b/ts/n3.lyx
index 8443b38..c287b3d 100644
--- a/ts/n3.lyx
+++ b/ts/n3.lyx
@@ -165,11 +165,11 @@ Las funciones
 \end_inset
 
  dadas por 
-\begin_inset Formula $f(x):=\tan(\frac{\pi}{2}x)$
+\begin_inset Formula $f(x)\coloneqq \tan(\frac{\pi}{2}x)$
 \end_inset
 
  y 
-\begin_inset Formula $g(x):=\frac{x}{1-x^{2}}$
+\begin_inset Formula $g(x)\coloneqq \frac{x}{1-x^{2}}$
 \end_inset
 
  son homeomorfismos.
@@ -177,7 +177,7 @@ Las funciones
 
 \begin_layout Enumerate
 Sea 
-\begin_inset Formula $N:=(0,\dots,0,1)\in\mathbb{R}^{n+1}$
+\begin_inset Formula $N\coloneqq (0,\dots,0,1)\in\mathbb{R}^{n+1}$
 \end_inset
 
 , la 
@@ -202,7 +202,7 @@ status open
 
 \begin_layout Plain Layout
 Sean 
-\begin_inset Formula $\pi:=\mathbb{R}^{n}\times\{-1\}$
+\begin_inset Formula $\pi\coloneqq \mathbb{R}^{n}\times\{-1\}$
 \end_inset
 
  y 
@@ -215,7 +215,7 @@ Sean
 \series default
  la proyección estereográfica.
  Si 
-\begin_inset Formula $y:=g(x)$
+\begin_inset Formula $y\coloneqq g(x)$
 \end_inset
 
 , 
@@ -309,7 +309,7 @@ Sean
 status open
 
 \begin_layout Plain Layout
-\begin_inset Formula $\mathbb{S}^{n}\setminus\{N\mid =(0,\dots,0,1)\}$
+\begin_inset Formula $\mathbb{S}^{n}\setminus\{N\coloneqq (0,\dots,0,1)\}$
 \end_inset
 
  y 
@@ -321,7 +321,7 @@ status open
 \end_inset
 
  y 
-\begin_inset Formula $\pi:=\mathbb{R}^{n}\times\{-1\}$
+\begin_inset Formula $\pi\coloneqq \mathbb{R}^{n}\times\{-1\}$
 \end_inset
 
 , son linealmente isomorfos, por lo que son homeomorfos y 
@@ -338,7 +338,7 @@ status open
 
 \begin_layout Enumerate
 El disco 
-\begin_inset Formula $\mathbb{D}^{n}:=\overline{B}_{d_{2}}(0;1)\subseteq\mathbb{R}^{n}$
+\begin_inset Formula $\mathbb{D}^{n}\coloneqq \overline{B}_{d_{2}}(0;1)\subseteq\mathbb{R}^{n}$
 \end_inset
 
  es homeomorfo a 
@@ -355,7 +355,7 @@ Sea
 \end_inset
 
  dada por 
-\begin_inset Formula $f(x):=x\frac{\Vert x\Vert_{\infty}}{\Vert x\Vert_{2}}$
+\begin_inset Formula $f(x)\coloneqq x\frac{\Vert x\Vert_{\infty}}{\Vert x\Vert_{2}}$
 \end_inset
 
  para 
@@ -363,7 +363,7 @@ Sea
 \end_inset
 
  y 
-\begin_inset Formula $f(0):=0$
+\begin_inset Formula $f(0)\coloneqq 0$
 \end_inset
 
 , queremos ver que 
@@ -371,7 +371,7 @@ Sea
 \end_inset
 
  es biyectiva con inversa 
-\begin_inset Formula $g(y):=y\frac{\Vert y\Vert_{2}}{\Vert y\Vert_{\infty}}$
+\begin_inset Formula $g(y)\coloneqq y\frac{\Vert y\Vert_{2}}{\Vert y\Vert_{\infty}}$
 \end_inset
 
  para 
@@ -723,7 +723,7 @@ unión disjunta
 \end_inset
 
  a 
-\begin_inset Formula $X\amalg Y:=(X\times\{0\})\cup(Y\times\{1\})$
+\begin_inset Formula $X\amalg Y\coloneqq (X\times\{0\})\cup(Y\times\{1\})$
 \end_inset
 
 .
@@ -736,7 +736,7 @@ unión disjunta
 \end_inset
 
  son espacios topológicos, definimos la topología 
-\begin_inset Formula ${\cal T}_{X\amalg Y}:=\{U\subseteq X\amalg Y\mid \{x\mid (x,0)\in U\}\in{\cal T}_{X}\land\{y\mid (y,1)\in U\}\in{\cal T}_{Y}\}$
+\begin_inset Formula ${\cal T}_{X\amalg Y}\coloneqq \{U\subseteq X\amalg Y\mid \{x\mid (x,0)\in U\}\in{\cal T}_{X}\land\{y\mid(y,1)\in U\}\in{\cal T}_{Y}\}$
 \end_inset
 
 .
@@ -806,11 +806,11 @@ Sea
 \end_inset
 
  dada por 
-\begin_inset Formula $f(x,0):=e^{x_{1}}v_{1}+\sum_{k=2}^{n}x_{k}v_{k}$
+\begin_inset Formula $f(x,0)\coloneqq e^{x_{1}}v_{1}+\sum_{k=2}^{n}x_{k}v_{k}$
 \end_inset
 
  y 
-\begin_inset Formula $f(y,0):=-e^{x_{1}}v_{1}+\sum_{k=2}^{n}x_{k}v_{k}$
+\begin_inset Formula $f(y,0)\coloneqq -e^{x_{1}}v_{1}+\sum_{k=2}^{n}x_{k}v_{k}$
 \end_inset
 
  es un homeomorfismo.
@@ -934,7 +934,7 @@ Sea
 \end_inset
 
 , 
-\begin_inset Formula $\{U_{i}\mid =\{x\mid (x,0)\in A_{i}\}\}_{i\in I}$
+\begin_inset Formula $\{U_{i}\coloneqq \{x\mid (x,0)\in A_{i}\}\}_{i\in I}$
 \end_inset
 
  lo es de 
@@ -947,7 +947,7 @@ Sea
 
 .
  Del mismo modo 
-\begin_inset Formula $\{V_{j}\mid =\{y\mid (y,1)\in A_{i}\}\}_{j\in I}$
+\begin_inset Formula $\{V_{j}\coloneqq \{y\mid (y,1)\in A_{i}\}\}_{j\in I}$
 \end_inset
 
  admite un subrecubrimiento finito 
@@ -1257,7 +1257,7 @@ Demostración:
 \end_inset
 
  dada por 
-\begin_inset Formula $f((x_{1},\dots,x_{m}),(y_{1},\dots,y_{n})):=(x_{1},\dots,x_{m},y_{1},\dots,y_{n})$
+\begin_inset Formula $f((x_{1},\dots,x_{m}),(y_{1},\dots,y_{n}))\coloneqq (x_{1},\dots,x_{m},y_{1},\dots,y_{n})$
 \end_inset
 
  es biyectiva.
@@ -1278,11 +1278,11 @@ Demostración:
 \end_inset
 
 , sean 
-\begin_inset Formula $a:=d_{\infty}(z,x)<\varepsilon_{x}$
+\begin_inset Formula $a\coloneqq d_{\infty}(z,x)<\varepsilon_{x}$
 \end_inset
 
  y 
-\begin_inset Formula $b:=d_{\infty}(w,y)<\delta_{y}$
+\begin_inset Formula $b\coloneqq d_{\infty}(w,y)<\delta_{y}$
 \end_inset
 
 , la bola 
@@ -1312,11 +1312,11 @@ Demostración:
 \end_inset
 
  dada por 
-\begin_inset Formula $f(L(x)):=(x,-1)$
+\begin_inset Formula $f(L(x))\coloneqq (x,-1)$
 \end_inset
 
  y 
-\begin_inset Formula $f(R(y)):=(y,1)$
+\begin_inset Formula $f(R(y))\coloneqq (y,1)$
 \end_inset
 
  es biyectiva.
@@ -1370,11 +1370,11 @@ proyecciones
 \end_inset
 
  dadas por 
-\begin_inset Formula $\pi_{1}(a,b):=a$
+\begin_inset Formula $\pi_{1}(a,b)\coloneqq a$
 \end_inset
 
  y 
-\begin_inset Formula $\pi_{2}(a,b):=b$
+\begin_inset Formula $\pi_{2}(a,b)\coloneqq b$
 \end_inset
 
  son continuas.
@@ -1416,7 +1416,7 @@ Sean
 \end_inset
 
  dada por 
-\begin_inset Formula $f(x):=(a(x),b(x))$
+\begin_inset Formula $f(x)\coloneqq (a(x),b(x))$
 \end_inset
 
  es continua si y sólo si lo son 
@@ -2144,7 +2144,7 @@ Demostración:
 
 .
  Sea 
-\begin_inset Formula $U:=\bigcap_{k=1}^{n}U_{y_{k}}$
+\begin_inset Formula $U\coloneqq \bigcap_{k=1}^{n}U_{y_{k}}$
 \end_inset
 
 , entonces 
@@ -2269,7 +2269,7 @@ Sean
 \end_inset
 
 , sea 
-\begin_inset Formula $I_{x}:=\{i\in I\mid x\in U_{i}\}$
+\begin_inset Formula $I_{x}\coloneqq \{i\in I\mid x\in U_{i}\}$
 \end_inset
 
 , 
@@ -2376,7 +2376,7 @@ proyección canónica
 aplicación cociente
 \series default
  
-\begin_inset Formula $p(x):=\overline{x}:=[x]$
+\begin_inset Formula $p(x)\coloneqq \overline{x}\coloneqq [x]$
 \end_inset
 
  que a cada 
@@ -2429,7 +2429,7 @@ Si
 \end_inset
 
 , llamamos 
-\begin_inset Formula $X/A:=X/\sim_{A}$
+\begin_inset Formula $X/A\coloneqq X/\sim_{A}$
 \end_inset
 
  donde 
@@ -2467,7 +2467,7 @@ Ejemplos:
 
 \begin_layout Enumerate
 Sea 
-\begin_inset Formula $X:=\mathbb{D}^{2}$
+\begin_inset Formula $X\coloneqq \mathbb{D}^{2}$
 \end_inset
 
 , 
@@ -2501,11 +2501,11 @@ para
 \end_inset
 
 , 
-\begin_inset Formula $f(0):=(0,0,1)$
+\begin_inset Formula $f(0)\coloneqq (0,0,1)$
 \end_inset
 
  y 
-\begin_inset Formula $f(*):=(0,0,-1)$
+\begin_inset Formula $f(*)\coloneqq (0,0,-1)$
 \end_inset
 
 .
@@ -2631,7 +2631,7 @@ Para
 \end_inset
 
 , sea 
-\begin_inset Formula $X:=[0,1]^{n}$
+\begin_inset Formula $X\coloneqq [0,1]^{n}$
 \end_inset
 
 , 
@@ -2643,7 +2643,7 @@ Para
 
 \begin_layout Enumerate
 Sean 
-\begin_inset Formula $X:=\mathbb{R}^{3}\setminus\{0\}$
+\begin_inset Formula $X\coloneqq \mathbb{R}^{3}\setminus\{0\}$
 \end_inset
 
  y 
@@ -2663,7 +2663,7 @@ Sean
 
 \begin_layout Standard
 Además, sea 
-\begin_inset Formula $X:=[0,1]\times[0,1]$
+\begin_inset Formula $X\coloneqq [0,1]\times[0,1]$
 \end_inset
 
 :