I'm reading appendixes A of O'Neill's book, "Semi-riemannian geometry" and I don't understand a something.
Where we use the assumption that $P$ is simply connected?
2026-03-25 19:04:06.1774465446
Question in the appendixes A of O'Neill book 2
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The assumption that $P$ is simply connected shows up when you show that that $\tilde{\phi}$ is a well defined continuous function.
Try it out when $\tilde{M} = \mathbb{R}, M = S^1$, and $P = S^1$ where the map $\tilde{M}\rightarrow S^1$ is the usual universal covering, and $P\rightarrow M$ is the identity.
Then the lift of the identity is discontinuous.