Moar puppy noses!
I was about to complain at your title that polyhedra are inherently geometric, not topological, but now that I see them, I agree, your name is appropriate. Those babies got higher homotopy.
Sounds like you’re several levels above me here. To google!
Topologists, man. You guys are wired differently from the rest of us. We amateurs all think donuts have holes.
I look at a topologist and realize that we live a different universes.
LOL donuts DO have holes.
See? I told you I don’t know what I am talking about.
I’m actually a geometer (which means I CAN tell my coffee cup from a donut).
Holes need to have a bottom or they’re simply negative space defined by some other object. The donut hole doesn’t exist because there’s no definition to it on at least 1 axis, no?
Oh it’s about to get real in here.
Tell that to those munchkins I’ve been eating.
Yummy donut holes. They’ve just been mass inverted.
Calling a cat a dog doesn’t make it bark. Nor does calling a dough ball a hole make it one
Just flavored hushpuppies
Years from now people will be saying “I remember how the topology war started back in 2021”.
No, well, I mean I guess you can define a hole differently than I do, but I would say a donut has a hole because if you loop a piece of string through there and tie it in a knot, you can’t pull it off without breaking the donut. In contrast, a fork does not have a hole. I would also say that “holes with a bottom,” as you say, are simply deformed disks, and not holes at all. There’s a notion of being able to put something through a hole that is being captured by my string-loop.
Oh, I expect that war much predates this conversation!
That’s an interesting view. The fork example is good because it has a bottom and a couple of sides but the space between the tines isn’t otherwise fully enclosed in a way to prevent the string from coming off.
So is a hole a thing with no mass or simply negative space that in some cases (donut) is called a hole and sometimes (fork) just space (although the dictionary definition of an aperture or gap would suggest that the fork has holes even though most people would not consider the slots to be holes)?
That means the hole is defined by the thing it is in vs any intrinsic characteristic and thus can only exist in a symbiotic relationship with another thing.
So is a hole in the ground or a cave or tunnel into (but not out of) the earth all deformed disks and not holes at all?
So if I swallow one end of a string… Nope! Not going to consider this further. Move along, nothing to see here.
I’ve got a hole in me pocket.
well, half a hole. I gave the other half to the nowhere man.
OK I actually laughed out loud.