As I understand it, the mathematical answer in modern physics is almost always zero, one, or infinity, regardless of the question being asked.
So as to the number of universes, take your pick.
If I had to guess, I’d go with zero. You’re all a figment of my imagination! 
That’s definitely a singularity. A regular fibration is pretty specific about what’s allowed as a fiber.
Really, what we’ve got here is an orbifold, as I’m sure Orbifold can tell you.
Small town idiot checking in here. My limited spacial intelligence tells me that a circle is defined as being 2-d, meaning it would have a height of “zero”. How then are we stacking these heightless shapes?
Remember, I’m none too smart, so take it easy on the vocab. if you don’t mind.
It’s the same as integration, really. Remember, the integral of a function over a single point is zero, but the integral over an interval may be non-zero.
The trick is that you’re dealing with measures here, and measures are only guaranteed to be countably additive.
Do you mind providing an example?
Firstly, a circle is one-dimensional. A disk is 2-d.
Now to your question, consider a unit square: the points in the plane with x- and y-coordinates both between 0 and 1. This is the union of a bunch of line segments. For every number x[sub]0[/sub] between 0 and 1, the segment l[sub]x[sub]0[/sub][/sub] = {(x[sub]0[/sub],y)| 0<=y<=1} is in the square, and the collection of all these (infinitely many) line segments makes up the square.
Now, consider the unit sphere. The naive way of chopping it up is (after removing the north and south poles) to break it into circles, each of which consists of the points at the same latitude. The problem is that those points at the poles aren’t circles, and they’re left out. The question is whether there’s a way of breaking the sphere into circles which doesn’t leave out any points, which it turns out can’t be done.
Thanks for the chopping up the sphere talk, that makes plenty of sense.
To continue the hijack…
Have patience with me on this circle thing, but I really do want to make sure I learn the correct definition.
About the 1-d circle, am I wrong in stating that all polygons are 2-d? What then causes the circle to be considered 1-d? The only difference I can see is that polygons must be made up of line segments.
You’re thinking of the interior of a circle: a disk. The circle is properly the edge of the disk.