A manifold is any topological space where, in the neighborhood of any point, (p), it is topologically equivalent (or homeomorphic) to a k-dimensional Euclidean space. We encountered the term manifold earlier in this book, but we didn't define it properly, so we will do that now. The preceding definition probably sounds a bit daunting, but it will make a lot more sense in a moment.
Suppose we have a one-dimensional manifold. For simplicity, we will work with a circle, or a disk, (which we denote as S1) that exists in 
(there are other one-dimensional manifolds, as well, such as parabolas, hyperbolas, and cubic curves, but that doesn't ...
