Mordred
Science Advisor
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WannabeNewton said:Again, this is not the kind of "lack of edge" that is being talked about. The Klein bottle is an example of a non-orientable manifold i.e. there doesn't exist a choice of nowhere-vanishing continuous n-form (volume form) on the manifold. This is not the same thing as saying the 3-sphere spatial sections of the closed universe model have "no edge"; the latter is just the statement that the 3-sphere has empty manifold boundary. It is finite in the sense that it is compact (every open cover has a finite subcover). Obviously the 3-sphere is orientable so this notion is not what is being talked about.
I agree with you on the points you made here. I posted the Klien bottle as an example of how a flat surface can have no edge.
We know the universe is close to flat there are 3 flat geometries that have no edge. The torus, the mobeous strip and the klien bottle.
Understanding flat geometry relations in cosmology is also important. As pointed out this has nothing to do with bounded, unbounded.
However it is important to be aware of. This also has little to do with the many worlds interpretation of the OP lol.
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