Sphere as the quotient space of a disk

Let's define an equivalence relation ~ on a disk (D^2) by stating that any two points on the boundary of a disk are equivalent. Obtained quotient space D^2/~=D^2/S^1 is homeomorphic to a 2-dimensional sphere (S^2).
One can also come up with the explicit quotient map, which is defined in the video.

[s.l.]

I think it is
int(D^2) = S^2 -{p}
where p is a point on S^2
So not quite S^2. It's S^2 minus a point.

[perriannesimkhovitch]

Points obscure themselves by inversional simple box cubic or face centered alternatives may introduce Penrose new fit, but some perspective will always be wiped out I guess not by translucence where hidden incidence optics manifests once more. Massive mounds of basalt perhaps is the Earth's answer to tetroginal versus hexagonal crisis of fit
Perhaps even giving rise to the inevitable heat death of entropy

[perriannesimkhovitch]

How many interpretive expressions in from the same geometry with their corresponding algebraic derivatives