update notations and fix typos

pages/Math4111/Math4111_L12.md

@@ -20,7 +20,7 @@ Proof:
 
 Fix $p\in X$, then $\{B_n(p)\}_{n\in \mathbb{N}}$ (specific open cover) is an open cover of $S$ (Since $\bigcup_{n\in \mathbb{N}}=X$). Since $S$ is compact, then $\exists$ a finite subcover ${n\in \mathbb{N}}_{i=1}^k=S$, let $r=max(n_1,...n_k)$, Then $S\subset B_r(p)$
 
-EOP
+QED
 
 #### Definition k-cell
 
@@ -74,7 +74,7 @@ Let $n\in \mathbb{N}$ be such that $\frac{1}{2^n}<r$. Then by $(c)$, $I(n)\subse
 
 Then $\{G_{\alpha_0}\}$ is a cover of $I_n$ which contradicts with (b)
 
-EOP
+QED
 
 #### Theorem 2.41
 
@@ -131,4 +131,4 @@ $$
 
 So $B_r(y)\cap S$ is finite. By **Theorem 2.20**, $y\notin  S$, this proves the claim so $S'\cap E=\phi$
 
-EOP
+QED