The Friedmann–Lemaître–Robertson–Walker (FLRW) metric - which was developed independently by the named authors in the 1920s and 1930s - describes a universe that is path-connected (it has a path from a point x to a point y in a topological space). But it's not necessarily simply connected.
Informally - if an object in space consists of one piece and does not have any "holes" that pass all the way through it, it is called simply connected. A doughnut (and the figure-8 Klein bottle it resembles) is “holey” and not simply connected (they're multiply connected). Referring to the infinite universe [see text associated with Figure 1] - a flat universe that is also simply connected implies an infinite universe. [Luminet, Jean-Pierre; Lachi`eze-Rey, Marc: “Cosmic Topology” - Physics Reports 254 (3): 135–214 (1995) arXiv:gr-qc/9605010] So it seems the infinite universe cannot be composed of topological subunits called figure-8 Klein bottles (flat universes that are finite in extent include the torus and Klein bottle). But the changing of the Klein bottle’s shape by binary digits composing photons and gravitons mimics the process of gaps in, or irregularities between, figure-8 Klein bottles being “filled in” by binary digits in the same way that computer drawings can extrapolate a small patch of blue sky to make a sky that’s blue from horizon to horizon. This ensures the positive and negative shapes in different figure-8 Klein bottles are precisely joined, and makes space-time relatively smooth and continuous as Einstein thought. Plus - it gets rid of holes, making figure-8 Klein subunits feasible.
(This is the beginning of the attached file, which contains 3,400 words - please feel free to read the file, or add your thoughts, or both.)
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Referring to the infinite universe - a flat universe that is also simply connected implies an infinite universe. [Luminet, Jean-Pierre; Lachi`eze-Rey, Marc: “Cosmic Topology” - Physics Reports 254 (3): 135–214 (1995) arXiv:gr-qc/9605010] So it seems the infinite universe cannot be composed of topological subunits called figure-8 Klein bottles (flat universes that are finite in extent include the torus and Klein bottle). But the changing of the Klein bottle’s shape by binary digits composing photons and gravitons mimics the process of gaps in, read more,..... worth for the time
The author are right
the infinite universe cannot be composed of topological subunits
The timeless and endless UNIVERSE were not created, it is here, and and will be here forever. It is natural that we Humans are afraid of the term of INFINITE whether it refers to space or time since we are well aver that it is beyond the reach of our understanding. The biggest problem however, that we tend do believe in an unsupportable idea of creation of something from nothing, and try to explain physical phenomenons, like in this case the gravitational force by assigning hypothetical "particles of which we have not yet proven its existence nor its mechanism.
Karoly Kehrer
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