As for topological dimension, roughly, if you consider a neighborhood of a point in the space, what does space look like from there? Locally it’s Euclidean if you’re “on” a manifold. The rigorous definition involves charts. See also Lebesgue covering dimension.
These are the best references I know:
Calculus on Manifolds
Boothby
As for topological dimension, roughly, if you consider a neighborhood of a point in the space, what does space look like from there? Locally it’s Euclidean if you’re “on” a manifold. The rigorous definition involves charts. See also Lebesgue covering dimension.