For each patch, a coordinate function maps the local coordinates to the euclidean space. Collection of all patches with coordinate functions covers the whole manifold.(adsbygoogle = window.adsbygoogle || []).push({});

What is a transition function and what is a change of coordinates?

Is it that you got one set of local coordinates throughout (?) the whole manifold and use a transition functions to show that the two coordinate functions are equal in the overlap regions? And does changing coordinates mean changing one set of local coordinates to another (x to x')?

Would be great if someone could help me out here. Thank you

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# Changing coordinates mean changing one set of local coordinates

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