updates

content/Math4111/Math4111_L7.md

@@ -80,7 +80,8 @@ Let $(X,d)$ be  a metric space, $\forall p\in X,\forall r>0$, $B_r(p)$ is an ope
 
 *every ball is an open set*
 
-Proof:
+<details>
+<summary>Proof</summary>
 
 Let $q\in B_r(p)$.
 
@@ -88,7 +89,7 @@ Let $h=r-d(p,q)$.
 
 Since $q\in B_r(p),h>0$. We claim that $B_h(q)$. Then $d(q,s)<h$, so $d(p,s)\leq d(p,q)+d(q,s)<d(p,q)+h=r$. (using triangle inequality) So $S\in B_r(p)$.
 
-QED
+</details>
 
 ### Closed sets