TITLE: is this set a regular surface?
QUESTION [5 upvotes]: I'm reading "Differential Geometry of Curves and Surfaces of Manfredo Docarmo" I'm doing  the exercises of the chapter 2. Here is the definition of regular surface that we are following: 
I have problems with this exercise: 
Is with the first part, I think that it's not true that it's a regular surface (the second it is). I don't know how to prove that something is not a regular surface.

REPLY [3 votes]: It is because in any neighborhood of a boundary point none of the orthogonal projections to the coordinate plane give a parametrization. This is a proposition in that section,and is often used to show that something is not a manifold.