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

---
 tem/n1.lyx | 16 ++++++++--------
 tem/n2.lyx |  6 +++---
 tem/n3.lyx |  6 +++---
 tem/n4.lyx | 10 +++++-----
 tem/n5.lyx |  6 +++---
 5 files changed, 22 insertions(+), 22 deletions(-)

(limited to 'tem')

diff --git a/tem/n1.lyx b/tem/n1.lyx
index 39659d7..e3a9d97 100644
--- a/tem/n1.lyx
+++ b/tem/n1.lyx
@@ -149,7 +149,7 @@ abiertos
 cerrados
 \series default
  a los complementarios de los abiertos: 
-\begin_inset Formula ${\cal C_{T}}:={\cal C}:=\{X\backslash A\}_{A\in{\cal T}}$
+\begin_inset Formula ${\cal C_{T}}\coloneqq {\cal C}\coloneqq \{X\backslash A\}_{A\in{\cal T}}$
 \end_inset
 
 .
@@ -370,7 +370,7 @@ La
 topología discreta
 \series default
 : 
-\begin_inset Formula ${\cal T}_{D}:={\cal P}(X)$
+\begin_inset Formula ${\cal T}_{D}\coloneqq {\cal P}(X)$
 \end_inset
 
 , la topología más grande que se puede definir sobre 
@@ -489,7 +489,7 @@ topología relativa
 topología de subespacio
 \series default
  como 
-\begin_inset Formula ${\cal T}|_{H}:={\cal T}_{H}:=\{A\cap H\}_{A\in{\cal T}}$
+\begin_inset Formula ${\cal T}|_{H}\coloneqq {\cal T}_{H}\coloneqq \{A\cap H\}_{A\in{\cal T}}$
 \end_inset
 
 .
@@ -671,7 +671,7 @@ Si
 
 .
  Pero si 
-\begin_inset Formula $C:=X\backslash A$
+\begin_inset Formula $C\coloneqq X\backslash A$
 \end_inset
 
 , entonces 
@@ -1381,7 +1381,7 @@ círculo
 \end_inset
 
  es el conjunto 
-\begin_inset Formula $C_{d}(p;r):=C(p;r):=\{x\in X\mid d(p,x)=r\}$
+\begin_inset Formula $C_{d}(p;r)\coloneqq C(p;r)\coloneqq \{x\in X\mid d(p,x)=r\}$
 \end_inset
 
 .
@@ -1402,7 +1402,7 @@ bola abierta
 \end_inset
 
  es el conjunto 
-\begin_inset Formula $B_{d}(p;r):=B(p;r):=\{x\in X\mid d(p,x)<r\}$
+\begin_inset Formula $B_{d}(p;r)\coloneqq B(p;r)\coloneqq \{x\in X\mid d(p,x)<r\}$
 \end_inset
 
 , y la 
@@ -1422,7 +1422,7 @@ bola cerrada
 \end_inset
 
  es el conjunto 
-\begin_inset Formula $\overline{B}_{d}(p;r):=\overline{B}(p;r):=B[p;r]:=\{x\in X\mid d(p,x)\leq r\}$
+\begin_inset Formula $\overline{B}_{d}(p;r)\coloneqq \overline{B}(p;r)\coloneqq B[p;r]\coloneqq \{x\in X\mid d(p,x)\leq r\}$
 \end_inset
 
 .
@@ -1707,7 +1707,7 @@ Demostración:
 
 .
  Ahora bien, si tomamos 
-\begin_inset Formula $r:=\min\{r_{1},\dots,r_{n}\}$
+\begin_inset Formula $r\coloneqq \min\{r_{1},\dots,r_{n}\}$
 \end_inset
 
 , vemos que 
diff --git a/tem/n2.lyx b/tem/n2.lyx
index 912a7be..82d69c9 100644
--- a/tem/n2.lyx
+++ b/tem/n2.lyx
@@ -1160,7 +1160,7 @@ Sea
 \end_inset
 
 , entonces 
-\begin_inset Formula $x\in\overline{S}\iff\exists\{x_{n}\}_{n=1}^{\infty}\subseteq S\mid x_{n}\rightarrow x$
+\begin_inset Formula $x\in\overline{S}\iff\exists\{x_{n}\}_{n=1}^{\infty}\subseteq S:x_{n}\rightarrow x$
 \end_inset
 
 .
@@ -1249,7 +1249,7 @@ Así pues, en un espacio métrico
 \end_inset
 
  si y sólo si 
-\begin_inset Formula $\forall x\in X,\exists\{x_{n}\}_{n=1}^{\infty}\subseteq S\mid x_{n}\rightarrow x$
+\begin_inset Formula $\forall x\in X,\exists\{x_{n}\}_{n=1}^{\infty}\subseteq S:x_{n}\rightarrow x$
 \end_inset
 
 , y 
@@ -1257,7 +1257,7 @@ Así pues, en un espacio métrico
 \end_inset
 
  si y sólo si 
-\begin_inset Formula $\exists\{x_{n}\}_{n=1}^{\infty}\subseteq S,\{y_{n}\}_{n=1}^{\infty}\subseteq X\backslash S\mid x_{n},y_{n}\rightarrow x$
+\begin_inset Formula $\exists\{x_{n}\}_{n=1}^{\infty}\subseteq S,\{y_{n}\}_{n=1}^{\infty}\subseteq X\backslash S:x_{n},y_{n}\rightarrow x$
 \end_inset
 
 .
diff --git a/tem/n3.lyx b/tem/n3.lyx
index 35cc0dc..89d965d 100644
--- a/tem/n3.lyx
+++ b/tem/n3.lyx
@@ -401,7 +401,7 @@ Sea
 
 .
  Podemos tomar 
-\begin_inset Formula $V'_{1}:=V_{1}\cap U_{1}\in{\cal E}(p)$
+\begin_inset Formula $V'_{1}\coloneqq V_{1}\cap U_{1}\in{\cal E}(p)$
 \end_inset
 
  y existirá 
@@ -1096,7 +1096,7 @@ biyectiva
 \end_inset
 
  Sea 
-\begin_inset Formula $g:=f^{-1}:Y\rightarrow X$
+\begin_inset Formula $g\coloneqq f^{-1}:Y\rightarrow X$
 \end_inset
 
  continua y 
@@ -1142,7 +1142,7 @@ biyectiva
 
 .
  Para ver que 
-\begin_inset Formula $g:=f^{-1}$
+\begin_inset Formula $g\coloneqq f^{-1}$
 \end_inset
 
  es continua, dado 
diff --git a/tem/n4.lyx b/tem/n4.lyx
index 2f3a2e7..3e83317 100644
--- a/tem/n4.lyx
+++ b/tem/n4.lyx
@@ -369,7 +369,7 @@ Demostración:
 \end_inset
 
  y definimos 
-\begin_inset Formula $G=\{x\in[a,b]|\exists\{A_{i_{1}},\dots,A_{i_{n}}\}\in{\cal P}_{0}({\cal A})\mid [a,x]\subseteq A_{i_{1}}\cup\dots\cup A_{i_{n}}\}$
+\begin_inset Formula $G=\{x\in[a,b]|\exists\{A_{i_{1}},\dots,A_{i_{n}}\}\in{\cal P}_{0}({\cal A}):[a,x]\subseteq A_{i_{1}}\cup\dots\cup A_{i_{n}}\}$
 \end_inset
 
 .
@@ -641,7 +641,7 @@ Demostración:
 
 .
  Sea entonces 
-\begin_inset Formula $A:=\bigcap_{i=1}^{r}A_{x_{i}}\in{\cal E}(p)$
+\begin_inset Formula $A\coloneqq \bigcap_{i=1}^{r}A_{x_{i}}\in{\cal E}(p)$
 \end_inset
 
 , dado 
@@ -1379,7 +1379,7 @@ teorema de la continuidad de la función inversa
 Demostración:
 \series default
  Basta probar que 
-\begin_inset Formula $g:=f^{-1}$
+\begin_inset Formula $g\coloneqq f^{-1}$
 \end_inset
 
  es continua.
@@ -1513,7 +1513,7 @@ Demostración:
 
 .
  Sea ahora 
-\begin_inset Formula $\delta'_{p}:=\frac{\delta_{p}}{2}$
+\begin_inset Formula $\delta'_{p}\coloneqq \frac{\delta_{p}}{2}$
 \end_inset
 
  y 
@@ -1529,7 +1529,7 @@ Demostración:
 \end_inset
 
 , y llamamos 
-\begin_inset Formula $\delta:=\min\{\delta'_{p_{1}},\dots,\delta'_{p_{r}}\}$
+\begin_inset Formula $\delta\coloneqq \min\{\delta'_{p_{1}},\dots,\delta'_{p_{r}}\}$
 \end_inset
 
 .
diff --git a/tem/n5.lyx b/tem/n5.lyx
index 93b40a3..8987d1f 100644
--- a/tem/n5.lyx
+++ b/tem/n5.lyx
@@ -813,7 +813,7 @@ criterio del peine
 \end_inset
 
 , entonces 
-\begin_inset Formula $H:=\bigcup_{i\in I}H_{i}$
+\begin_inset Formula $H\coloneqq \bigcup_{i\in I}H_{i}$
 \end_inset
 
  es conexo.
@@ -950,7 +950,7 @@ En particular, si
 \end_inset
 
  entonces 
-\begin_inset Formula $H:=\bigcup_{i\in I}H_{i}$
+\begin_inset Formula $H\coloneqq \bigcup_{i\in I}H_{i}$
 \end_inset
 
  es conexo, y si 
@@ -1128,7 +1128,7 @@ convexo
 segmento
 \series default
  
-\begin_inset Formula $L_{xy}:=\{(1-t)x+ty\}_{t\in[0,1]}$
+\begin_inset Formula $L_{xy}\coloneqq \{(1-t)x+ty\}_{t\in[0,1]}$
 \end_inset
 
  es un subconjunto de 
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