Differential Forms On The Cross
Friday, December 7, 2018
In this note, we describe the differential 1-forms on X = ox ∪ oy, the diffeological subspace in R2 consisting of the reunion of the axes ox and oy. We show that every 1-form α on X is the restriction of a form A on R2, :
 α = A | X 
A = a(x) dx + b(y) dy.

Ref. http://math.huji.ac.il/~piz/documents/DBlog-Rmk-DFOTC.pdf