Suppose C is a collection of coordinate systems for M such that (1) For each x 1028 M there is f 1028 C which is a coordinate system around (2) if f, g 1028 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 1028 C ...

Define the orientation to be the for every and with In order for this to be well def ...

Suppose C is a collection of coordinate systems for M such that (1) For each x Є

Question:

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.