Update documentation

_sources/book/topology/001-metric-spaces.md

@@ -447,8 +447,8 @@ Let $(X, d_X)$ be a {prf:ref}`metric space<topology:def-metric-space>`.
 Then
 
 1. The empty set $\emptyset$ and $X$ are open,
-2. If $\{U_i\}_{i \in I}$ is a collection of open sets, then $\cup{i \in I} U_i$ is open,
-3. If $U_1, \ldots, U_N$ are open sets, then $\cap{n = 1}^N U_n$ is open.
+2. If $\{U_i\}_{i \in I}$ is a collection of open sets, then $\bigcup{i \in I} U_i$ is open,
+3. If $U_1, \ldots, U_N$ are open sets, then $\bigcap{n = 1}^N U_n$ is open.
 :::
 
 :::{dropdown} Proof: Properties of open sets
@@ -466,4 +466,4 @@ Let $U_1, \ldots, U_N$ be open sets.
 Suppose $x \in \cap_{n = 1}^N U_n.$
 Then, $x \in U_n$ for all $n = 1, \ldots, N,$ so there exists $r_n > 0$ such that $B_{r_n}(x) \subseteq U_n$ for all $n = 1, \ldots, N.$
 Taking $r = \min\{r_1, \ldots, r_N\},$ we have that $B_r(x) \subseteq U_n$ for all $n = 1, \ldots, N,$ so $\cap_{n = 1}^N U_n$ is open.
-:::
+:::

book/topology/001-metric-spaces.html

@@ -884,8 +884,8 @@ <h2>Open and closed sets<a class="headerlink" href="#open-and-closed-sets" title
 Then</p>
 <ol class="arabic simple">
 <li><p>The empty set <span class="math notranslate nohighlight">\(\emptyset\)</span> and <span class="math notranslate nohighlight">\(X\)</span> are open,</p></li>
-<li><p>If <span class="math notranslate nohighlight">\(\{U_i\}_{i \in I}\)</span> is a collection of open sets, then <span class="math notranslate nohighlight">\(\cup{i \in I} U_i\)</span> is open,</p></li>
-<li><p>If <span class="math notranslate nohighlight">\(U_1, \ldots, U_N\)</span> are open sets, then <span class="math notranslate nohighlight">\(\cap{n = 1}^N U_n\)</span> is open.</p></li>
+<li><p>If <span class="math notranslate nohighlight">\(\{U_i\}_{i \in I}\)</span> is a collection of open sets, then <span class="math notranslate nohighlight">\(\bigcup{i \in I} U_i\)</span> is open,</p></li>
+<li><p>If <span class="math notranslate nohighlight">\(U_1, \ldots, U_N\)</span> are open sets, then <span class="math notranslate nohighlight">\(\bigcap{n = 1}^N U_n\)</span> is open.</p></li>
 </ol>
 </section>
 </div><details class="sd-sphinx-override sd-dropdown sd-card sd-mb-3">