On Thu, Jan 23, 2020 at 6:40 AM Alan Grayson <[email protected]> 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 -- 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/CAJPayv1xaVUAHJt5rjL0cjpd7zP-tQ4MzpW12MDVMZSSG3E28w%40mail.gmail.com.
