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Zheyuan Wu
2026-03-20 16:59:05 -05:00
parent cd8705ad9e
commit 3f4479157b
9 changed files with 250 additions and 27 deletions

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@@ -163,9 +163,9 @@ 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)\}