1. The problem statement, all variables and given/known data http://imgur.com/goozE9f 2. Relevant equations ##(dx_i)_p i= 1,2,3## 3. The attempt at a solution I'm reading Manfredo and Do Carmo's Differential Forms and Applications. This is the very first page Would you mind explaining me what is meant by dx, as highlighted in the picture? I guess it is "differential", like in Calculus textbooks, but what kind of mathematical object is it? A set, a line, a point? What is its domain? How is it formalized? Instances of compose the space's basis. Are they arbitrary, or should they be selected in some way? PS: Is there any way to post the image here without uploading it to your server?