A Few Half-Lines
Sunday, April 21, 2013
 
With Enxin Wu, we compared various diffeologies on the half-line [0,∞[,. The ones coming from the quotients ∆n = Rn/O(n), the one coming from the limit of these spaces ∆∞ = lim (∆n), and the subset diffeology ∆ = [0,∞[ ⊂ R. We observe that ∆ and ∆∞ do not coincide, and we have the following strict chain of diffeological spaces ∆1 ≺ ∆2 ≺ … ≺ ∆∞ ≺ ∆. Ref. http://math.huji.ac.il/~piz/documents/DBlog-Rmk-AFHL.pdf