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Zheyuan Wu
2026-02-18 11:51:28 -06:00
parent e7dc80a673
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3 changed files with 66 additions and 1 deletions

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@@ -23,7 +23,7 @@ Let $p: E\to B$ be a covering map, and $e_0\in E$ and $p(e_0)=b_0$. Any path $f:
Back to the circle example, it means that there exists a unique correspondence between a loop starting at $(1,0)$ in $S^1$ and a path in $\mathbb{R}$ starting at $0$, ending in $\mathbb{Z}$.
<details>
<summary>Proof</summary>
<summary>Idea for Proof</summary>
Starting at $b_0$, by the covering map property, there exist some open neighborhood $U_0$ of $b_0$ such that $V_0=p^{-1}(U_0)$ is a neighborhood of $e_0$. And $p|_{V_0}$ is a homeomorphism on to $U_0$.