I'm looking for some guidance for a relatively simple question. We are supposed to describe the boundary points, the interior points, and state whether or not it is open, closed, or neither.
So I draw each of these individually and restrict my focus to the overlapping areas. For x≥0, I get all x values greater than and equal to 0 in the y-z plane. For y<0 I get all values of y less than and not equal to 0 in the x-z plane. The overlapping portion of 3 space ends up being 2 octants.
bdry(S) is the set of points (x,0) such that x≥0, and the set of points (0,y) such that 0≥y.
Wouldnt the interior of S be the overlapping octants such that y<0, and hence all the points not touching the x-axis?
Solution says it would be points not touching the y-axis, but I am not seeing it.