This “wrapping a leash around the hole” action that Snoopy can perform is actually a group action of \(\mathbb{Z}\) on the base space (Bobs space): For each integer \(n \in \mathbb{Z}\), Snoopy can wrap the leash around the hole \(n\) times, and \(n-m\) corresponds to Snoopy walking around the hole \(n\) times clockwise and then \(m\) times counterclockwise.
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