diff options
Diffstat (limited to 'ggs')
| -rw-r--r-- | ggs/n2.lyx | 8 | ||||
| -rw-r--r-- | ggs/n3.lyx | 10 | ||||
| -rw-r--r-- | ggs/n4.lyx | 4 | ||||
| -rw-r--r-- | ggs/n5.lyx | 2 | ||||
| -rw-r--r-- | ggs/n7.lyx | 2 |
5 files changed, 13 insertions, 13 deletions
@@ -569,7 +569,7 @@ intervalo maximal de existencia Demostración: \series default Sea -\begin_inset Formula ${\cal J}_{p,v}:=\{(I,\alpha):\alpha:I\to S\text{ geodésica},0\in I,\alpha(0)=p,\alpha'(0)=v\}$ +\begin_inset Formula ${\cal J}_{p,v}:=\{(I,\alpha)\mid \alpha\mid I\to S\text{ geodésica},0\in I,\alpha(0)=p,\alpha'(0)=v\}$ \end_inset . @@ -669,7 +669,7 @@ Sean ahora es abierto y, por el teorema del peine, también conexo, luego es un intervalo. Sea -\begin_inset Formula $A:=\{t\in I_{1}\cap I_{2}:\alpha_{1}(t)=\alpha_{2}(t),\alpha'_{1}(t)=\alpha'_{2}(t)\}$ +\begin_inset Formula $A:=\{t\in I_{1}\cap I_{2}\mid \alpha_{1}(t)=\alpha_{2}(t),\alpha'_{1}(t)=\alpha'_{2}(t)\}$ \end_inset , y queremos ver que @@ -1401,7 +1401,7 @@ geodésicamente completa \begin_layout Enumerate Dado el plano -\begin_inset Formula $S=\{p\in\mathbb{R}^{3}:\langle p,a\rangle=c\}$ +\begin_inset Formula $S=\{p\in\mathbb{R}^{3}\mid \langle p,a\rangle=c\}$ \end_inset , la geodésica maximal de @@ -1579,7 +1579,7 @@ Sean \end_inset , -\begin_inset Formula $S:=\{(x,y,z)\in\mathbb{R}^{3}:x^{2}+y^{2}=r^{2}\}$ +\begin_inset Formula $S:=\{(x,y,z)\in\mathbb{R}^{3}\mid x^{2}+y^{2}=r^{2}\}$ \end_inset un cilindro, @@ -110,7 +110,7 @@ aplicación exponencial \end_inset donde -\begin_inset Formula ${\cal D}_{p}:=\{v\in T_{p}S:1\in I_{v}\}$ +\begin_inset Formula ${\cal D}_{p}:=\{v\in T_{p}S\mid 1\in I_{v}\}$ \end_inset . @@ -909,7 +909,7 @@ Sean \end_inset tal que -\begin_inset Formula ${\cal D}(0,r):=\{v\in T_{p}S:\Vert v\Vert<r\}\subseteq{\cal D}_{p}$ +\begin_inset Formula ${\cal D}(0,r):=\{v\in T_{p}S\mid \Vert v\Vert<r\}\subseteq{\cal D}_{p}$ \end_inset , llamamos @@ -933,7 +933,7 @@ disco geodésico \end_inset cumple que -\begin_inset Formula ${\cal S}(0,r):=\{v\in T_{p}S:\Vert v\Vert=r\}\subseteq{\cal D}_{p}$ +\begin_inset Formula ${\cal S}(0,r):=\{v\in T_{p}S\mid \Vert v\Vert=r\}\subseteq{\cal D}_{p}$ \end_inset , llamamos @@ -1099,7 +1099,7 @@ Sean \end_inset , luego -\begin_inset Formula $t_{0}=\max\{t\in[a,b]:\alpha(t)=p_{0}\}<b$ +\begin_inset Formula $t_{0}=\max\{t\in[a,b]\mid \alpha(t)=p_{0}\}<b$ \end_inset (pues @@ -1422,7 +1422,7 @@ Finalmente, sea es \begin_inset Formula \[ -A:=\{t\in(a,b):\Vert\tilde{\alpha}(t)\Vert=r^{*}\}=\{t\in[a,b]:\alpha(t)\in S(p_{0},r^{*})\}\neq\emptyset. +A:=\{t\in(a,b)\mid \Vert\tilde{\alpha}(t)\Vert=r^{*}\}=\{t\in[a,b]\mid \alpha(t)\in S(p_{0},r^{*})\}\neq\emptyset. \] \end_inset @@ -258,7 +258,7 @@ Demostración: \begin_layout Standard Primero vemos que -\begin_inset Formula $A:=\{q\in S:\Omega(p,q)\neq\emptyset\}=S$ +\begin_inset Formula $A:=\{q\in S\mid \Omega(p,q)\neq\emptyset\}=S$ \end_inset viendo que es abierto, cerrado y no vacío. @@ -750,7 +750,7 @@ Queremos ver que \end_inset , existe -\begin_inset Formula $t^{*}:=\inf\{t\in[a,b]:\alpha(t)\notin D(p,r^{*})\}$ +\begin_inset Formula $t^{*}:=\inf\{t\in[a,b]\mid \alpha(t)\notin D(p,r^{*})\}$ \end_inset , pero @@ -229,7 +229,7 @@ Demostración: \end_inset y -\begin_inset Formula $A:=\{t\in[0,1]:\tilde{\alpha}(t)=tw\}$ +\begin_inset Formula $A:=\{t\in[0,1]\mid \tilde{\alpha}(t)=tw\}$ \end_inset , queremos ver que @@ -273,7 +273,7 @@ soporte \end_inset es -\begin_inset Formula $\text{sop}f:=\overline{\{x\in D:f(x)\neq0\}}$ +\begin_inset Formula $\text{sop}f:=\overline{\{x\in D\mid f(x)\neq0\}}$ \end_inset . |