Manifold/rewrite

This is a proposed rewrite of manifold. Of course, all the deleted parts have to be found a home in some other article, such as Manifold/rewrite/topological manifold or Manifold/rewrite/differentiable manifold

Related Topics:
Manifold - Manifold/rewrite/topological manifold - Manifold/rewrite/differentiable manifold

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Target audience (roughly):

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

• For lead section and examples: high school.
• For Topological manifolds and Smooth manifolds: first-year or second-year undergraduates.
• For the rest: graduates.

You are welcome to edit it.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~