29 Jun '10 16:20>1 edit
Originally posted by adam warlockIn spaces like R^3, yes, but I thought you meant in isolation (i.e. in the space formed by itself). In R^3 it's straightforward that it is bounded and has a boundary so in no way is it boundless.
I don't think I understood you. The surface of a sphere does have a boundary. And a sphere does have a boundary too. I'm using regular topological definitions.
Is this a case of the same words being used in different contexts type of confusion? 😕
So, at best, I can interpret your claim of a sphere being boundless as not having a boundary in isolation but if you go to it as a subset of a larger space then I don't see how you can in any meaningful way say it is boundless.