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cianfa72

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Hi,

a basic question related to differential manifold definition.

Leveraging on the atlas's charts ##\left\{(U_i,\varphi_i)\right\} ## we actually define on ##M## the notion of differentiable function. Now take a specific chart ##\left(U,\varphi \right)## and consider a function ##f## defined on it that happens to be

My question is: for the given function defined on ##M## could it be the case in resulting differentiable when represented in another atlas's chart (e.g. in the ##\left(V,\gamma \right)## chart supposed to be compatible with ##\left(U,\varphi \right)## )?

In other words: we know the notion of differentiable function is compatible across charts belonging to the same differential structure, but what about a

Thanks

a basic question related to differential manifold definition.

Leveraging on the atlas's charts ##\left\{(U_i,\varphi_i)\right\} ## we actually define on ##M## the notion of differentiable function. Now take a specific chart ##\left(U,\varphi \right)## and consider a function ##f## defined on it that happens to be

*not*differentiable in that specific chart.My question is: for the given function defined on ##M## could it be the case in resulting differentiable when represented in another atlas's chart (e.g. in the ##\left(V,\gamma \right)## chart supposed to be compatible with ##\left(U,\varphi \right)## )?

In other words: we know the notion of differentiable function is compatible across charts belonging to the same differential structure, but what about a

*not*differentiable function as represented in one of the charts ?Thanks

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