I found this inside a proof of another fact. I've been trying to find any result to prove it, but I couldn't find any. Does someone know this result or how to prove it? I'm working with a manifold inside $W^{1,p}(\Omega)$, if it can help by any way.
2026-03-28 13:27:18.1774704438
Every banach manifold is locally arcwise conneted
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Every Banach space has the property that all its open balls are locally convex, hence arcwise-connected. So all Banach manifolds are locally arcwise-connected too.