We know that 2 Möbius-Strips can be joined edge-wise to eliminate that edge producing 0 Edge topological structure.
ML (Möbius Left) + MR (Möbius Right) = KOJ (Simple "inverted sock" Klein Bottle)
ML + ML = K8L-O (Left-handed figure-8 Klein bottle)
MR + MR = K8R-O (Right-handed figure-8 Klein bottle)
Now I have "possibly naive" questions. Edges can be eliminated by joining them, can this analogy be used for joining surfaces. That is going by normal imagination overlapping 2 surface leads to decrease in number of total surface. So my questions -
So are there any topological structures with "zero" surfaces.
Can this be achieved by joining opposite/ similar chiral/ non-chiral Klein bottles.
What will be properties of such topological structure.
Please note that I have by no means deep understanding of topology and only have superficial knowledge that I gained by browsing through some videos or relatively simple papers. So please be lenient if my questions are not well formed.