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<title>proof by vuorilehto</title>
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  <title>Homotopy Invariance of the Fundamental Groupoid</title>
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<p>Let <img src="https://latex.codecogs.com/png.latex?X"> and <img src="https://latex.codecogs.com/png.latex?Y"> be topological spaces.</p>
<div id="thm-induced" class="theorem">
<p><span class="theorem-title"><strong>Theorem 1 (Induced Functors)</strong></span> A continuous map <img src="https://latex.codecogs.com/png.latex?f%20:%20X%20%5Cto%20Y"> induces a well-defined functor: <img src="https://latex.codecogs.com/png.latex?%5CPi_1(f)%20:%20%5CPi_1(X)%20%5Cto%20%5CPi_1(Y)"></p>
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<p><span class="proof-title"><em>Proof</em>. </span>For every path class <img src="https://latex.codecogs.com/png.latex?%5B%5Cgamma%5D%20%5Cin%20%5CPi_1(X)(x_0,%20x_1)">, define <img src="https://latex.codecogs.com/png.latex?%5CPi_1(f)(%5B%5Cgamma%5D)%20=%20%5Bf%20%5Ccirc%20%5Cgamma%5D">…</p>
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  <category>topology</category>
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  <pubDate>Fri, 04 Sep 2026 21:00:00 GMT</pubDate>
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  <dc:creator>Harlow Malloc</dc:creator>
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<p>This is a post with executable code.</p>



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  <title>Welcome To My Blog</title>
  <dc:creator>Tristan O&#39;Malley</dc:creator>
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  <pubDate>Tue, 01 Sep 2026 21:00:00 GMT</pubDate>
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