diff options
Diffstat (limited to 'ts/n1.lyx')
| -rw-r--r-- | ts/n1.lyx | 26 |
1 files changed, 13 insertions, 13 deletions
@@ -268,7 +268,7 @@ entorno \end_inset es un elemento de -\begin_inset Formula ${\cal E}(x):=\{U\in{\cal T}:x\in{\cal U}\}$ +\begin_inset Formula ${\cal E}(x):=\{U\in{\cal T}\mid x\in{\cal U}\}$ \end_inset . @@ -459,7 +459,7 @@ abierta a \begin_inset Formula \[ -B_{d}(x,\delta):=\{y\in X:d(x,y)<\varepsilon\}. +B_{d}(x,\delta):=\{y\in X\mid d(x,y)<\varepsilon\}. \] \end_inset @@ -485,7 +485,7 @@ inducida \end_inset a la topología -\begin_inset Formula ${\cal T}_{d}:=\{A\in X:\forall x\in A,\exists\delta>0:B_{d}(x,\delta)\subseteq A\}$ +\begin_inset Formula ${\cal T}_{d}:=\{A\in X\mid \forall x\in A,\exists\delta>0\mid B_{d}(x,\delta)\subseteq A\}$ \end_inset . @@ -578,7 +578,7 @@ La -esfera \series default , -\begin_inset Formula $\mathbb{S}^{n}(r):=\{(x_{1},\dots,x_{n+1})\in\mathbb{R}^{n+1}:x_{1}^{2}+\dots+x_{n+1}^{2}=r^{2}\}$ +\begin_inset Formula $\mathbb{S}^{n}(r):=\{(x_{1},\dots,x_{n+1})\in\mathbb{R}^{n+1}\mid x_{1}^{2}+\dots+x_{n+1}^{2}=r^{2}\}$ \end_inset . @@ -630,7 +630,7 @@ El cilindro \series default , -\begin_inset Formula $C:=\{(x,y,z)\in\mathbb{R}^{3}:x^{2}+y^{2}=1,0\leq z\leq1\}$ +\begin_inset Formula $C:=\{(x,y,z)\in\mathbb{R}^{3}\mid x^{2}+y^{2}=1,0\leq z\leq1\}$ \end_inset , cono de rotación sobre el eje @@ -666,7 +666,7 @@ El toro \series default , -\begin_inset Formula $\mathbb{T}:=\{(x,y,z)\in\mathbb{R}^{3}:x^{2}+y^{2}+z^{2}-4\sqrt{x^{2}+y^{2}}+3=0\}$ +\begin_inset Formula $\mathbb{T}:=\{(x,y,z)\in\mathbb{R}^{3}\mid x^{2}+y^{2}+z^{2}-4\sqrt{x^{2}+y^{2}}+3=0\}$ \end_inset , cono de rotación sobre el eje @@ -674,7 +674,7 @@ toro \end_inset de -\begin_inset Formula $\{(x,0,z):(x-2)^{2}+z^{2}=1\}$ +\begin_inset Formula $\{(x,0,z)\mid (x-2)^{2}+z^{2}=1\}$ \end_inset . @@ -695,7 +695,7 @@ status open \end_inset Tenemos -\begin_inset Formula $\{(x,0,z):(x-2)^{2}+z^{2}=1\}=\{\alpha(s):=(\cos s+2,0,\sin s)\}_{s\in[0,2\pi]}$ +\begin_inset Formula $\{(x,0,z)\mid (x-2)^{2}+z^{2}=1\}=\{\alpha(s)\mid =(\cos s+2,0,\sin s)\}_{s\in[0,2\pi]}$ \end_inset , luego el cono de rotación es @@ -1056,7 +1056,7 @@ Como los abiertos en \end_inset , -\begin_inset Formula $s^{-1}((a,b))=\{(x,y):a<s(x,y)=x+y<b\}=\{(x,y):a-x<y<b-x\}$ +\begin_inset Formula $s^{-1}((a,b))=\{(x,y)\mid a<s(x,y)=x+y<b\}=\{(x,y)\mid a-x<y<b-x\}$ \end_inset . @@ -1135,7 +1135,7 @@ Dado \end_inset , queremos ver que -\begin_inset Formula $p^{-1}((a,b))=\{(x,y):a<p(x,y)=xy<b\}$ +\begin_inset Formula $p^{-1}((a,b))=\{(x,y)\mid a<p(x,y)=xy<b\}$ \end_inset es abierto. @@ -1217,7 +1217,7 @@ Basta ver que, dada una bola , su inversa es un abierto. Tenemos -\begin_inset Formula $d^{-1}(B_{d_{\infty}}(y,r))=\{x:d_{\infty}((x,\dots,x),y)<r\}=\{t:|x-y_{1}|,\dots,|x-y_{n}|<r\}$ +\begin_inset Formula $d^{-1}(B_{d_{\infty}}(y,r))=\{x\mid d_{\infty}((x,\dots,x),y)<r\}=\{t\mid |x-y_{1}|,\dots,|x-y_{n}|<r\}$ \end_inset , pero @@ -2043,7 +2043,7 @@ topología generada \end_inset a -\begin_inset Formula ${\cal T}_{{\cal B}}:=\{U\subseteq X:\forall x\in U,\exists B\in{\cal B}:x\in B\subseteq U\}$ +\begin_inset Formula ${\cal T}_{{\cal B}}:=\{U\subseteq X\mid \forall x\in U,\exists B\in{\cal B}\mid x\in B\subseteq U\}$ \end_inset , y se tiene que @@ -2456,7 +2456,7 @@ Dada una base \end_inset numerable, -\begin_inset Formula ${\cal B}_{x}:=\{B\in{\cal B}:x\in B\}$ +\begin_inset Formula ${\cal B}_{x}:=\{B\in{\cal B}\mid x\in B\}$ \end_inset es base de entornos de |