Ah yes, the olde Everett Scheme. Lavish with universes.
Frankly I think Everett was not speaking topology like a native, nor do very many cosmologists today.
For, let |G(obs)| be the naive norm of the set of all universes which are observationally or existentially (experientially) indistinguishable, G(0bs). Let Gt^u be the set of all universes, up to some proper time ‘t’ which are consistent with each other (i.e. consistent with the history of all particle trajectories). If you are in one of the Gt’s you could be in any of them, up to your own time ‘t’. Now let Heff be the set of effective hamiltonians which give the same physical results (a very large number of members, since for many orders of magnitude of the most fundamental physical constants there will be no effective difference in results among any of them) as are actually observed. My claim is |G(obs)| = |Gt^u/Heff| i.e. this norm is the ‘size’ of the consistent set Gt^u modulo the Heff’s (setting them all, as it were, to be identical), and that this norm is close to 1.00 (not needing therefore more sophisticated re-normalization). Thus insofar as it makes any physical sense (mathematics here be damned because of our aforementioned topological considerations — i.e. with math we can make the math be irrelevant), the universe is unique.

Ah yes, the olde Everett Scheme. Lavish with universes.

Frankly I think Everett was not speaking topology like a native, nor do very many cosmologists today.

For, let |G(obs)| be the naive norm of the set of all universes which are observationally or existentially (experientially) indistinguishable, G(0bs). Let Gt^u be the set of all universes, up to some proper time ‘t’ which are consistent with each other (i.e. consistent with the history of all particle trajectories). If you are in one of the Gt’s you could be in any of them, up to your own time ‘t’. Now let Heff be the set of effective hamiltonians which give the same physical results (a very large number of members, since for many orders of magnitude of the most fundamental physical constants there will be no effective difference in results among any of them) as are actually observed. My claim is |G(obs)| = |Gt^u/Heff| i.e. this norm is the ‘size’ of the consistent set Gt^u modulo the Heff’s (setting them all, as it were, to be identical), and that this norm is close to 1.00 (not needing therefore more sophisticated re-normalization). Thus insofar as it makes any physical sense (mathematics here be damned because of our aforementioned topological considerations — i.e. with math we can make the math be irrelevant), the universe is unique.