It is well known that every $C^1$ manifold admits a smooth manifold structure. What if we relax the definition of smooth manifold so the transition maps need only be differentiable? Does every such "differentiable manifold" admit a compatible $C^1$ atlas?
2026-04-14 05:17:19.1776143839
Are there "differentiable manifolds" that don't admit a $C^1$-structure
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