I was wondering if someone could help with this question. I am stuck on part of the question showing that the following set is a regular surface in

i.e. the affine plane through a point p spanned by linearly independent vectors.

In particular I am trying to show that the function , given by is a homeomorphism. I think its clear that it is bijective and continuous but I am having difficulty showing that it's inverse is continuous, that is for some open set O ,

for some open set E in . How do I find out what E must be?

any help would be appreciated