define a space for the surface of a sphere with fewer than 3 dimensions.

latitude and longitude

such a map is guaranteed to not be a bijection

just put the poles wherever it’s convenient

idk, to me this is kinda semantics, whether or not we say a 2d surface in 3d space is 2d or 3d.

just assume “straight line” refers to a geodesic on the surface, then you can use whatever coordinates you want.