I'm trying to get an idea on how the dunce hat works. I'd like to compute $\pi_1$, $H_n$, and its universal covering space. Any ideas on what these will look like?
2026-03-25 07:42:57.1774424577
Topological structure of the dunce hat
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The wikipedia page mentions that it is contractible. It follows that $\pi_1$ is trivial and $H_0\cong \mathbb{Z}$ and $H_i=0$ for $i\not=0$. The universal cover is the space itself.