O'Reilly logo

Exterior Analysis by Erdogan Suhubi

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

Example 2.3.3. The manifold image in image will now be considered. We know that this sphere can only be homeomorphic to the plane image by employing two charts of its atlas and two differentiable functions ϕ1, ϕ2 given below:

image

[see pp. 81-82]. Thus, we cannot find a single diffeomorphism. Hence, the sphere cannot be diffeomorphic to the plane. On the other hand, ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required