1

I understand that a region of type 1 is where two curves are connected by two vertical lines and that a region of type 2 is where two curves are connected by two horizontal lines. But what is a region of type 3?

Keighleyite
  • 321

1 Answers1

-1

A region of type III is both type I and type II.

Jürgen Sukumaran
  • 7,645
  • So would that be a rectangle with four straight edges? Or a blob with four curves? Or are they both regions of type 3? – Keighleyite Apr 24 '19 at 14:12
  • 1
    A rectangle is definitely a type III region but not all type III regions are rectangles. A blob with four curves as you've described could be considered a type III region if it is closed and contained in some ellipse. – Jürgen Sukumaran Apr 24 '19 at 14:25
  • @TSF I do not understand why the blob you describe is a type III region. In this context a type I region is of the form $D = {(x,y)|a\leq x \leq b, g_1(x)\leq y \leq g_2(x) }$ and similar for II but in y. Could you expand on in what sense the blob is both type I and type II? – Salamander Jan 26 '21 at 15:30
  • It means it consists of four curves but they are not constrained to be straight lines. – Jürgen Sukumaran Jan 26 '21 at 18:23