updates

content/Math4202/Math4202_L9.md

@@ -7,7 +7,7 @@
 Consider the space of paths up to homotopy equivalence.
 
 $$
-\operatorname{Path}/\simeq_p(X) =\Pi_1(X)
+\operatorname{Path}/\simeq_p(X) =pi_1(X)
 $$
 
 We want to impose some group structure on $\operatorname{Path}/\simeq_p(X)$.
@@ -33,9 +33,9 @@ Define the product $f*g$ of $f$ and $g$ to be the map $h:[0,1]\to X$.
 
 #### Definition for equivalent classes of paths
 
-$\Pi_1(X,x)$ is the equivalent classes of paths starting and ending at $x$.
+$pi_1(X,x)$ is the equivalent classes of paths starting and ending at $x$.
 
-On $\Pi_1(X,x)$,, we define $\forall [f],[g],[f]*[g]=[f*g]$.
+On $pi_1(X,x)$,, we define $\forall [f],[g],[f]*[g]=[f*g]$.
 
 $$
 [f]\coloneqq \{f_i:[0,1]\to X|f_0(0)=f(0),f_i(1)=f(1)\}
@@ -141,5 +141,5 @@ Continue next time.
 The fundamental group of $X$ at $x$ is defined to be
 
 $$
-(\Pi_1(X,x),*)
+(pi_1(X,x),*)
 $$