In the definition of smooth manifolds we require that the transition functions between different charts be infinitely differentiable (a circle is an example of such a manifold). Topological manifolds, however, does not require transitions functions to be smooth (or rather no transition functions at all), but just out of curiosity are there examples of simple topological manifolds (like the square) which have transition functions between different charts, but where these are not smooth?(adsbygoogle = window.adsbygoogle || []).push({});

I tried to find some for the square, but I can not seem to find charts that overlap (the edges are in the way). Is this a general phenomenon?

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# Example of a topological manifold without smooth transition functions.

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