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atom.xml

@@ -1,13 +1,15 @@
 <?xml version="1.0" encoding="utf-8"?>
 <feed xmlns="http://www.w3.org/2005/Atom"><title>eigenℝic</title><link href="https://eigenric.me/" rel="alternate"></link><link href="https://eigenric.me/atom.xml" rel="self"></link><id>https://eigenric.me/</id><updated>2024-11-26T00:00:00+01:00</updated><entry><title>El grupo fundamental de la cinta de Möbius</title><link href="https://eigenric.me/blog/2024/11/el-grupo-fundamental-de-la-cinta-de-mobius" rel="alternate"></link><published>2024-11-26T00:00:00+01:00</published><updated>2024-11-26T00:00:00+01:00</updated><author><name>Ricardo Ruiz Fernández de Alba</name></author><id>tag:eigenric.me,2024-11-26:/blog/2024/11/el-grupo-fundamental-de-la-cinta-de-mobius</id><summary type="html">&lt;p&gt;&lt;br&gt;&lt;/p&gt;
-&lt;p&gt;&lt;center&gt;&lt;/p&gt;
-&lt;iframe width="500" height="300" src="https://www.youtube.com/embed/savG0a_MijQ?si=29DqwxaXU0VHxF2e" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen&gt;&lt;/iframe&gt;
-&lt;p&gt;&lt;/center&gt;&lt;/p&gt;
+&lt;div class="video-responsive"&gt;
+&lt;iframe src="https://www.youtube.com/embed/savG0a_MijQ?si=29DqwxaXU0VHxF2e" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen&gt;&lt;/iframe&gt;
+&lt;/div&gt;
+
 &lt;p&gt;La cinta de Möbius es una superficie no orientable que ha fascinado a matemáticos debido a sus propiedades geométricas y topológicas singulares&lt;/p&gt;
 &lt;p&gt;Esta figura se obtiene al darle una media …&lt;/p&gt;</summary><content type="html">&lt;p&gt;&lt;br&gt;&lt;/p&gt;
-&lt;p&gt;&lt;center&gt;&lt;/p&gt;
-&lt;iframe width="500" height="300" src="https://www.youtube.com/embed/savG0a_MijQ?si=29DqwxaXU0VHxF2e" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen&gt;&lt;/iframe&gt;
-&lt;p&gt;&lt;/center&gt;&lt;/p&gt;
+&lt;div class="video-responsive"&gt;
+&lt;iframe src="https://www.youtube.com/embed/savG0a_MijQ?si=29DqwxaXU0VHxF2e" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen&gt;&lt;/iframe&gt;
+&lt;/div&gt;
+
 &lt;p&gt;La cinta de Möbius es una superficie no orientable que ha fascinado a matemáticos debido a sus propiedades geométricas y topológicas singulares&lt;/p&gt;
 &lt;p&gt;Esta figura se obtiene al darle una media vuelta a una tira de papel y unir sus extremos y presenta características inusuales cuando se estudian desde la topología. &lt;/p&gt;
 &lt;p&gt;El grupo fundamental de un espacio topológico &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;X&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;span aria-hidden="true" class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut" style="height:0.6833em;"&gt;&lt;/span&gt;&lt;span class="mord mathnormal" style="margin-right:0.07847em;"&gt;X&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;, &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mi mathvariant="normal"&gt;Π&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mo separator="true"&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;\Pi_1(X, x_0)&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;span aria-hidden="true" class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut" style="height:1em;vertical-align:-0.25em;"&gt;&lt;/span&gt;&lt;span class="mord"&gt;&lt;span class="mord"&gt;Π&lt;/span&gt;&lt;span class="msupsub"&gt;&lt;span class="vlist-t vlist-t2"&gt;&lt;span class="vlist-r"&gt;&lt;span class="vlist" style="height:0.3011em;"&gt;&lt;span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"&gt;&lt;span class="pstrut" style="height:2.7em;"&gt;&lt;/span&gt;&lt;span class="sizing reset-size6 size3 mtight"&gt;&lt;span class="mord mtight"&gt;1&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="vlist-s"&gt;​&lt;/span&gt;&lt;/span&gt;&lt;span class="vlist-r"&gt;&lt;span class="vlist" style="height:0.15em;"&gt;&lt;span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal" style="margin-right:0.07847em;"&gt;X&lt;/span&gt;&lt;span class="mpunct"&gt;,&lt;/span&gt;&lt;span class="mspace" style="margin-right:0.1667em;"&gt;&lt;/span&gt;&lt;span class="mord"&gt;&lt;span class="mord mathnormal"&gt;x&lt;/span&gt;&lt;span class="msupsub"&gt;&lt;span class="vlist-t vlist-t2"&gt;&lt;span class="vlist-r"&gt;&lt;span class="vlist" style="height:0.3011em;"&gt;&lt;span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"&gt;&lt;span class="pstrut" style="height:2.7em;"&gt;&lt;/span&gt;&lt;span class="sizing reset-size6 size3 mtight"&gt;&lt;span class="mord mtight"&gt;0&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="vlist-s"&gt;​&lt;/span&gt;&lt;/span&gt;&lt;span class="vlist-r"&gt;&lt;span class="vlist" style="height:0.15em;"&gt;&lt;span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;  describe las clases de homotopía de lazos cerrados y es un invariante topológico crucial para caracterizar su estructura. &lt;/p&gt;
@@ -69,7 +71,7 @@ r_0(x,y) = (x, 0)
 &lt;p&gt;&lt;span class="katex-display"&gt;&lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;math display="block" xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;mo stretchy="false"&gt;[&lt;/mo&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo separator="true"&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;mo separator="true"&gt;,&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;mo stretchy="false"&gt;]&lt;/mo&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo stretchy="false"&gt;[&lt;/mo&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo separator="true"&gt;,&lt;/mo&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;mo stretchy="false"&gt;]&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;π&lt;/mi&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo separator="true"&gt;,&lt;/mo&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;
 H([(x,y), s)]) = [(x, (1-s)y)] = \pi(x, (1-s)y)
 &lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;span aria-hidden="true" class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut" style="height:1em;vertical-align:-0.25em;"&gt;&lt;/span&gt;&lt;span class="mord mathnormal" style="margin-right:0.08125em;"&gt;H&lt;/span&gt;&lt;span class="mopen"&gt;([(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;x&lt;/span&gt;&lt;span class="mpunct"&gt;,&lt;/span&gt;&lt;span class="mspace" style="margin-right:0.1667em;"&gt;&lt;/span&gt;&lt;span class="mord mathnormal" style="margin-right:0.03588em;"&gt;y&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;span class="mpunct"&gt;,&lt;/span&gt;&lt;span class="mspace" style="margin-right:0.1667em;"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;s&lt;/span&gt;&lt;span class="mclose"&gt;)])&lt;/span&gt;&lt;span class="mspace" style="margin-right:0.2778em;"&gt;&lt;/span&gt;&lt;span class="mrel"&gt;=&lt;/span&gt;&lt;span class="mspace" style="margin-right:0.2778em;"&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="base"&gt;&lt;span class="strut" style="height:1em;vertical-align:-0.25em;"&gt;&lt;/span&gt;&lt;span class="mopen"&gt;[(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;x&lt;/span&gt;&lt;span class="mpunct"&gt;,&lt;/span&gt;&lt;span class="mspace" style="margin-right:0.1667em;"&gt;&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord"&gt;1&lt;/span&gt;&lt;span class="mspace" style="margin-right:0.2222em;"&gt;&lt;/span&gt;&lt;span class="mbin"&gt;−&lt;/span&gt;&lt;span class="mspace" style="margin-right:0.2222em;"&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="base"&gt;&lt;span class="strut" style="height:1em;vertical-align:-0.25em;"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;s&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;span class="mord mathnormal" style="margin-right:0.03588em;"&gt;y&lt;/span&gt;&lt;span class="mclose"&gt;)]&lt;/span&gt;&lt;span class="mspace" style="margin-right:0.2778em;"&gt;&lt;/span&gt;&lt;span class="mrel"&gt;=&lt;/span&gt;&lt;span class="mspace" style="margin-right:0.2778em;"&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="base"&gt;&lt;span class="strut" style="height:1em;vertical-align:-0.25em;"&gt;&lt;/span&gt;&lt;span class="mord mathnormal" style="margin-right:0.03588em;"&gt;π&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;x&lt;/span&gt;&lt;span class="mpunct"&gt;,&lt;/span&gt;&lt;span class="mspace" style="margin-right:0.1667em;"&gt;&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord"&gt;1&lt;/span&gt;&lt;span class="mspace" style="margin-right:0.2222em;"&gt;&lt;/span&gt;&lt;span class="mbin"&gt;−&lt;/span&gt;&lt;span class="mspace" style="margin-right:0.2222em;"&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="base"&gt;&lt;span class="strut" style="height:1em;vertical-align:-0.25em;"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;s&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;span class="mord mathnormal" style="margin-right:0.03588em;"&gt;y&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
-&lt;p&gt;Claramente &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;H&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;span aria-hidden="true" class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut" style="height:0.6833em;"&gt;&lt;/span&gt;&lt;span class="mord mathnormal" style="margin-right:0.08125em;"&gt;H&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; es continua por ser composición de funcioness continuas y además:&lt;/p&gt;
+&lt;p&gt;Claramente &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;H&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;span aria-hidden="true" class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut" style="height:0.6833em;"&gt;&lt;/span&gt;&lt;span class="mord mathnormal" style="margin-right:0.08125em;"&gt;H&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; es continua por ser composición de funciones continuas y además:&lt;/p&gt;
 &lt;p&gt;&lt;span class="katex-display"&gt;&lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;math display="block" xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;mo stretchy="false"&gt;[&lt;/mo&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo separator="true"&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;mo stretchy="false"&gt;]&lt;/mo&gt;&lt;mo separator="true"&gt;,&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo stretchy="false"&gt;[&lt;/mo&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo separator="true"&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;mo stretchy="false"&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;
 H([(x,y)], 0) = [(x,y)]
 &lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;span aria-hidden="true" class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut" style="height:1em;vertical-align:-0.25em;"&gt;&lt;/span&gt;&lt;span class="mord mathnormal" style="margin-right:0.08125em;"&gt;H&lt;/span&gt;&lt;span class="mopen"&gt;([(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;x&lt;/span&gt;&lt;span class="mpunct"&gt;,&lt;/span&gt;&lt;span class="mspace" style="margin-right:0.1667em;"&gt;&lt;/span&gt;&lt;span class="mord mathnormal" style="margin-right:0.03588em;"&gt;y&lt;/span&gt;&lt;span class="mclose"&gt;)]&lt;/span&gt;&lt;span class="mpunct"&gt;,&lt;/span&gt;&lt;span class="mspace" style="margin-right:0.1667em;"&gt;&lt;/span&gt;&lt;span class="mord"&gt;0&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;span class="mspace" style="margin-right:0.2778em;"&gt;&lt;/span&gt;&lt;span class="mrel"&gt;=&lt;/span&gt;&lt;span class="mspace" style="margin-right:0.2778em;"&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="base"&gt;&lt;span class="strut" style="height:1em;vertical-align:-0.25em;"&gt;&lt;/span&gt;&lt;span class="mopen"&gt;[(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;x&lt;/span&gt;&lt;span class="mpunct"&gt;,&lt;/span&gt;&lt;span class="mspace" style="margin-right:0.1667em;"&gt;&lt;/span&gt;&lt;span class="mord mathnormal" style="margin-right:0.03588em;"&gt;y&lt;/span&gt;&lt;span class="mclose"&gt;)]&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

blog.html

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blog/2013/index.html

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blog/2017/08/una-odisea-de-depuracion-top-down-con-vim.html

@@ -21,7 +21,7 @@
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blog/2017/09/index.html

@@ -11,7 +11,7 @@
 
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