Also, if we do not treat E^n as a vector space, then the difference in this space is somewhat undefined. MW> No. You are assuming difference in E^n is a binary operation, whereas MW> it is a mapping into R^n.
It all depends on how you define it. The difference in E^n is in E^n, and since noone distinguishes E^n and R^n, you can say that the difference is in R^n. Anyway, this is getting further and further away from the original question. There is something wrong if we try to distinguish E^n from R^n, talking about a GUI library.
I probably used the wrong word there. By *point* I meant "an element", and element in R^n is a vector. You can not have "points" in R^n, which are not vectors. MW> So we seem to agree.
Kind of. We are down to E^n vs R^n, which according to most literature is the same space, and according to some lecture notes are different spaces. Valentin Samko http://val.samko.info