On Friday, January 24, 2020 at 6:38:43 PM UTC-7, Alan Grayson wrote: > > Both are connected. Both have no boundary. Both are closed, since both > contain their accumulation points. Both have uncountable elements. So how > can they be distinguished within the context of point-set topology? TIA, AG >
One way to distinguish the two surfaces is the fact that on a sphere, the path starting at any point, closes on itself, unlike the starting point on a plane. But what if the sphere is distorted, suppose it looks like potato. For a potato-shaped "sphere", this distinguishing feature fails. So the question remains. And the answer is, what? TIA, AG -- 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/705cb549-33fc-4d89-8d5f-c03ca3d1d18d%40googlegroups.com.
