diff options
Diffstat (limited to 'ts/n6.lyx')
| -rw-r--r-- | ts/n6.lyx | 62 | 
1 files changed, 31 insertions, 31 deletions
| @@ -317,7 +317,7 @@ Sea  .   Sea  -\begin_inset Formula $v:=t_{1}v_{1}+\dots+t_{k}v_{k}\in[v_{1},\dots,v_{k}]$ +\begin_inset Formula $v\coloneqq t_{1}v_{1}+\dots+t_{k}v_{k}\in[v_{1},\dots,v_{k}]$  \end_inset  . @@ -345,7 +345,7 @@ Sea  .   En otro caso,  -\begin_inset Formula $w:=\frac{t_{1}}{1-t_{k}}v_{1}+\dots+\frac{t_{k-1}}{1-t_{k}}v_{k-1}\in\text{conv}\{v_{1},\dots,v_{k-1}\}\subseteq\text{conv}\{v_{1},\dots,v_{k}\}\subseteq C$ +\begin_inset Formula $w\coloneqq \frac{t_{1}}{1-t_{k}}v_{1}+\dots+\frac{t_{k-1}}{1-t_{k}}v_{k-1}\in\text{conv}\{v_{1},\dots,v_{k-1}\}\subseteq\text{conv}\{v_{1},\dots,v_{k}\}\subseteq C$  \end_inset  , luego  @@ -385,12 +385,12 @@ símplice  vértices  \series default  , en posición general,  -\begin_inset Formula $[v_{0},\dots,v_{k}]:=\text{conv}\{v_{0},\dots,v_{k}\}$ +\begin_inset Formula $[v_{0},\dots,v_{k}]\coloneqq \text{conv}\{v_{0},\dots,v_{k}\}$  \end_inset  .   Si  -\begin_inset Formula $v:=t_{0}v_{0}+\dots+t_{k}v_{k}\in[v_{0},\dots,v_{k}]$ +\begin_inset Formula $v\coloneqq t_{0}v_{0}+\dots+t_{k}v_{k}\in[v_{0},\dots,v_{k}]$  \end_inset   con cada  @@ -418,7 +418,7 @@ coordinadas baricéntricas  \begin_layout Standard  Si  -\begin_inset Formula $W:=\{v_{0},\dots,v_{k}\}$ +\begin_inset Formula $W\coloneqq \{v_{0},\dots,v_{k}\}$  \end_inset   determina un  @@ -648,7 +648,7 @@ característica de Euler  \end_inset   es  -\begin_inset Formula $\chi(T):=i_{0}-i_{1}+\dots+(-1)^{n}i_{n}$ +\begin_inset Formula $\chi(T)\coloneqq i_{0}-i_{1}+\dots+(-1)^{n}i_{n}$  \end_inset  . @@ -721,19 +721,19 @@ status open  \begin_layout Plain Layout  En efecto, sean  -\begin_inset Formula $a:=(0,0,1)$ +\begin_inset Formula $a\coloneqq (0,0,1)$  \end_inset  ,  -\begin_inset Formula $b:=(0,1,-1)$ +\begin_inset Formula $b\coloneqq (0,1,-1)$  \end_inset  ,  -\begin_inset Formula $c:=(-1,-1,-1)$ +\begin_inset Formula $c\coloneqq (-1,-1,-1)$  \end_inset   y  -\begin_inset Formula $d:=(1,-1,-1)$ +\begin_inset Formula $d\coloneqq (1,-1,-1)$  \end_inset  , entonces el complejo simplicial dado por  @@ -746,7 +746,7 @@ En efecto, sean  \end_inset  junto con el homeomorfismo  -\begin_inset Formula $h(x,y,z):=\frac{(x,y,z)}{|(x,y,z)|}$ +\begin_inset Formula $h(x,y,z)\coloneqq \frac{(x,y,z)}{|(x,y,z)|}$  \end_inset   forman una triangulación de  @@ -831,7 +831,7 @@ Presentaciones poligonales  \begin_layout Standard  Sea  -\begin_inset Formula $S:=\overline{B_{d_{1}}}(0;1)$ +\begin_inset Formula $S\coloneqq \overline{B_{d_{1}}}(0;1)$  \end_inset  . @@ -927,7 +927,7 @@ Una  presentación poligonal  \series default   es una expresión de la forma  -\begin_inset Formula ${\cal P}:=\langle S\mid W_{1},\dots,W_{k}\rangle$ +\begin_inset Formula ${\cal P}\coloneqq \langle S\mid W_{1},\dots,W_{k}\rangle$  \end_inset  , donde  @@ -995,7 +995,7 @@ Para cada palabra  \end_inset  , sea  -\begin_inset Formula $n_{i}:=|W_{i}|$ +\begin_inset Formula $n_{i}\coloneqq |W_{i}|$  \end_inset  . @@ -1028,7 +1028,7 @@ Si  \end_inset   dados por  -\begin_inset Formula $a_{ij}:=[v_{ij},v_{i(j+1)}]$ +\begin_inset Formula $a_{ij}\coloneqq [v_{ij},v_{i(j+1)}]$  \end_inset   entendiendo  @@ -1036,7 +1036,7 @@ Si  \end_inset  , y el polígono  -\begin_inset Formula $P_{i}:=\text{conv}\{v_{i1},\dots,v_{in_{i}}\}$ +\begin_inset Formula $P_{i}\coloneqq \text{conv}\{v_{i1},\dots,v_{in_{i}}\}$  \end_inset  . @@ -1076,7 +1076,7 @@ Si  \end_inset   disjuntos (salvo en los puntos inicial y final), y  -\begin_inset Formula $P_{i}:=\text{conv}\{a_{ij}(s)\}_{s\in[0,1]}^{j\in\{1,2\}}$ +\begin_inset Formula $P_{i}\coloneqq \text{conv}\{a_{ij}(s)\}_{s\in[0,1]}^{j\in\{1,2\}}$  \end_inset  . @@ -1090,7 +1090,7 @@ Sea  .   Tomamos el espacio topológico  -\begin_inset Formula $X:=(P_{1}\amalg\dots\amalg P_{k})/\sim$ +\begin_inset Formula $X\coloneqq (P_{1}\amalg\dots\amalg P_{k})/\sim$  \end_inset  , donde  @@ -1233,7 +1233,7 @@ aristas  \end_inset   son regiones poligonales,  -\begin_inset Formula $P:=P_{1}\amalg\dots\amalg P_{k}$ +\begin_inset Formula $P\coloneqq P_{1}\amalg\dots\amalg P_{k}$  \end_inset   y  @@ -1716,39 +1716,39 @@ status open  \begin_layout Plain Layout  Sean  -\begin_inset Formula $a_{0}:=(0,1,0)$ +\begin_inset Formula $a_{0}\coloneqq (0,1,0)$  \end_inset  ,  -\begin_inset Formula $a_{1}:=(0,3,1)$ +\begin_inset Formula $a_{1}\coloneqq (0,3,1)$  \end_inset  ,  -\begin_inset Formula $a_{2}:=(0,3,-1)$ +\begin_inset Formula $a_{2}\coloneqq (0,3,-1)$  \end_inset  ,  -\begin_inset Formula $b_{0}:=(-1,-1,0)$ +\begin_inset Formula $b_{0}\coloneqq (-1,-1,0)$  \end_inset  ,  -\begin_inset Formula $b_{1}:=(-3,-3,1)$ +\begin_inset Formula $b_{1}\coloneqq (-3,-3,1)$  \end_inset  ,  -\begin_inset Formula $b_{2}:=(-3,-3,-1)$ +\begin_inset Formula $b_{2}\coloneqq (-3,-3,-1)$  \end_inset  ,  -\begin_inset Formula $c_{0}:=(1,-1,0)$ +\begin_inset Formula $c_{0}\coloneqq (1,-1,0)$  \end_inset  ,  -\begin_inset Formula $c_{1}:=(3,-3,1)$ +\begin_inset Formula $c_{1}\coloneqq (3,-3,1)$  \end_inset   y  -\begin_inset Formula $c_{2}:=(3,-3,-1)$ +\begin_inset Formula $c_{2}\coloneqq (3,-3,-1)$  \end_inset  . @@ -1764,7 +1764,7 @@ Sean  y cuyas aristas y vértices son los subsímplices de estas caras.   Entonces, si  -\begin_inset Formula $r:=\frac{29}{20}$ +\begin_inset Formula $r\coloneqq \frac{29}{20}$  \end_inset  , la circunferencia  @@ -1794,11 +1794,11 @@ y cuyas aristas y vértices son los subsímplices de estas caras.  .   Entonces, si  -\begin_inset Formula $p(x,y):=r(\frac{x}{\sqrt{x^{2}+y^{2}}},\frac{y}{\sqrt{x^{2}+y^{2}}},0)$ +\begin_inset Formula $p(x,y)\coloneqq r(\frac{x}{\sqrt{x^{2}+y^{2}}},\frac{y}{\sqrt{x^{2}+y^{2}}},0)$  \end_inset  , la función  -\begin_inset Formula $h(x,y,z):=r(x,y)+\frac{(x,y,z)-r(x,y)}{|(x,y,z)-r(x,y)|}$ +\begin_inset Formula $h(x,y,z)\coloneqq r(x,y)+\frac{(x,y,z)-r(x,y)}{|(x,y,z)-r(x,y)|}$  \end_inset   es un homeomorfismo del complejo al toro con circunferencia interior  | 
