Bachman : A geometric approach to differential forms

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SUMMARY

Bachman's book presents a vector in the tangent space as dx(0,1) + dy(1,0) on page 18. This notation is correct and intentional, as it reflects the standard convention in differential geometry for representing vectors in tangent spaces. The alternative expression dx(1,0) + dy(0,1) is not used because it does not align with the established coordinate system and basis vectors in the context of differential forms. Understanding this distinction is crucial for accurately interpreting differential forms and their applications.

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mrslamovics
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Forms and basis in TpC (page 18)
Hi All!
First of all , sorry for my English :)
In Bachman's book, on page 18, a vector in the tangent space is written in the form dx(0,1)+dy(1,0). Why is it not written the other way around, so why isn’t dx(1,0)+dy(0,1) the correct expression? Thank you.
 
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It looks like a typo.
 
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Thanks a lot!
 

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