Skip to content

Commit

Permalink
fix: missed closing for math
Browse files Browse the repository at this point in the history
  • Loading branch information
cuppajoeman committed Oct 27, 2024
1 parent 2b2a585 commit d640732
Showing 1 changed file with 1 addition and 1 deletion.
2 changes: 1 addition & 1 deletion html/topology/interior_and_closure.html
Original file line number Diff line number Diff line change
Expand Up @@ -120,7 +120,7 @@
Suppose that \( A \) is a subset of a topological space, then we have \[ \operatorname{Int}\left( A \right) \subseteq A \subseteq \bar{A} \]
</div>
<div class="proof">
<p> Let A be a subset of the topological space \(X\). Let \(x\) be an arbitrary point in \(int(A)\). By definition, there exist an open ball \(B_\epsilon(p)) such that \(B_\epsilon(p)\subseteq A\). Since the open ball is entirely contained in \(A\), \(x\) must be an element of A. Since (\bar{A}=A^*\cup A\) by definition, since \(x\) is in A, \(x\in \bar{A}\). Since \(x\), which is an element of the interior of A, was chosen arbitrarily, the interior of A is a subset of A and is a subset of the closure.
<p> Let A be a subset of the topological space \(X\). Let \(x\) be an arbitrary point in \(int(A)\). By definition, there exist an open ball \(B_\epsilon(p)\) such that \(B_\epsilon(p)\subseteq A\). Since the open ball is entirely contained in \(A\), \(x\) must be an element of A. Since (\bar{A}=A^*\cup A\) by definition, since \(x\) is in A, \(x\in \bar{A}\). Since \(x\), which is an element of the interior of A, was chosen arbitrarily, the interior of A is a subset of A and is a subset of the closure.
</p>
</div>
</div>
Expand Down

0 comments on commit d640732

Please sign in to comment.