If $y\in \partial (\mathbb D^2)$, then how to find $\pi_1(\mathbb D^2-\{y\})$? I know that if $y$ was an interior point then the answer will be $\mathbb Z$. But why both cases would be similar ?
2026-03-31 19:15:08.1774984508
The fundamental group of the unit disc with one point removed from its boundary
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It's pretty obvious that your space is contractible: you can deformation retract it to the centre along straight lines, say. Thus its fundamental group is trivial.