1
$\begingroup$

I want to prove that we can not make a perfect 2-dimensional map of the earth, to achieve this I have figured out that I must prove there is not a homeomorphism from the surface of a sphere to the 2-dimensional plane, but how can I prove this?

$\endgroup$
1
  • $\begingroup$ What did you try? $\endgroup$ Commented Jun 4, 2018 at 11:46

1 Answer 1

1
$\begingroup$

The sphere and the plane are not homeomorphic to each other; the sphere is compact, the plane isn't. Actually, the question has been answered more generally:

Why the surface of the sphere is not a Euclidean space?

$\endgroup$
0

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .