3D space interface to other dimensions

[snorkack]

There are some theories which claim that space should for some mathematical reason have more than 3+1 dimensions, but that some of them are for some reasons "rolled up".
How would an interface look like where the number of unrolled dimensions changes?
Consider a blister on skin, or paint. The interior of the blister is a 3D region. Skin outside the blister is 2D. So the edge of the blister is a 1D line.
But the interior of the blister has actual bounding surfaces in the 3rd dimension. If on approaching the edge of 3D space, the 3rd dimension is "rolled up" rather than terminated at the ends, how would you see the difference?
The interior of black holes is said to have 3 dimensions instead of 4 (3+1), so event horizon is precisely a 2D surface where the 3+1D space terminates.
And how would a surface look like where 1 rolled-up space dimension unrolls? Looking from 3D space towards a region of 4D space?

 

[EventHorizon]

Imagine it this way: a race of flat beings were living inside a two-dimensional picture. Even if the picture was extremely beautiful and eye-catching, they could only see the world around them; in their eyes, everything was simply line segments of various lengths and thicknesses. When one two-dimensional object is taken out of the picture into three-dimensional space would it see the entirety of the image if it just looks down.

Notable writer Cixin Liu described 4D like this:
Those who had never experienced 4D space might get the wrong impression that they were seeing everything "through" the hull (the characters are in a spaceship). But no, they were not seeing "through" anything. Everything was laid out in the open, just like when we look at a circle drawn on a piece of paper, we can see the inside of a circle without looking "through" anything. This kind of openness extended to every level, and the hardest part was describing how it applied to solid objects. One could see the interior of solids, such as the bulkheads or a piece of metal or a rock---one could see all the cross sections at once!

 

[Drakkith]

Your question is somewhat unclear, as there are no 'edges' to space in either the 3D model or the 3+n D model where n rolled up dimensions exist.