> Yet, this common-sense definition is unsatisfying if we consider that a lower-dimensional object might end up straddling a higher-dimensional space. If a line segment is rotated or bent, does that make it 2D? Or is that object forever one-dimensional, somehow retaining the memory of its original orientation and curvature?
Isn't that exactly what topological manifolds are for?
Isn't that exactly what topological manifolds are for?
https://en.wikipedia.org/wiki/Manifold