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Suppose C is a collection of coordinate

Suppose C is a collection of coordinate systems for M such that (1) For each x Є M there is f Є C which is a coordinate system around ; (2) if f, g Є C, then det (f -1 0 g) 2 > 0. Show that there is a unique orientation of M such that is orientation-preserving for all f Є C.

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