On Thursday, January 23, 2020 at 8:47:25 AM UTC-6, John Clark wrote: > > On Thu, Jan 23, 2020 at 6:40 AM Alan Grayson <[email protected] > <javascript:>> wrote: > > >>Lawrence Crowell wrote: *I would say the spatial surface is >>> topologically closed, but not causally closed. * >> >> >> *> As I just posted, this is correct, but can you give a precise >> mathematical meaning to "topologically closed"? TIA, AG * >> > > The Universe is topologically closed if you can give me any point in the > universe I can give you a number greater than zero that you can use as a > radius to draw a sphere centered on that point such that every point within > that sphere is also in the universe. Or to put it more succinctly, if the > universe is topologically closed then it would contain all its limit > points. But you want to know if it's finite or infinite and this would tell > you nothing about that. > > John K Clark >
AKA Heine-Borel theorem. LC -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/92080a5c-8d2b-43f7-9b33-b91399d7806e%40googlegroups.com.
