I don’t think that distinction exists, SentientMeat. Smoothly deform a human as follows: Open the mouth really wide. Prolapse the inside of the mouth cavity, to the point where the connection to the nasal passages is outside. Migrate the mouth end of the nasal passage to elsewhere on the body. You now have two “separate” holes through the manifold, just as if you had a stigma. But since the deformations were all smooth, we haven’t changed the topology at all, so those extra holes were there and “separate” to begin with.
But Chronos, The mouth is still one hole.
There is the hole mouth to anus and the hole mouth to nostrils. For there to be two distinct holes one would have to stitch the mouth in the middle somewhere. I get what you are trying to say, but from the way I see it, you would end up essentially with a sphere with a “H” shaped hole in it (mouth, anus and two nostrils). No matter which way you manipulate it I can’t see how you can separate the mouth - nostril connection.
Flowch
Nobody’s trying to separate the mouth-nostril connection. (Did I really just type that?) It’s just that every hole in an object is topologically equivalent. Mouth-to-anus is a hole, nostril-to-nostril is a hole, they’re all the same.
Picture it this way: You’ve got a donut made of infintely stretchable clay. You can squeeze the clay around to one side to make a really lopsided donut. Then you can make an indentation and turn it into a coffee cup. And you haven’t poked any extra holes in the thing, so you haven’t changed it topologically. But it will never be a two-handled sugar bowl.
(Special thanks to my uncle for letting me spend hours with his Time-Life science series of books, and then giving them to me several years ago.)
Great minds think alike–and so does mine.
Yes. And ironically, topology is the only math (besides logic) I was ever good at.
I can also turn a mobius strip into a pretty watermelon-fruit-basket looking thing.
Of course, I’m not as cool as the guy who makes real-life glass klein bottle beer steins.
Apparently, mytopology dorkdom lives on to this day. Learn to make pretty colored world maps with only 4 crayons. Find a whole list of children’s lit that’s topology oriented. Be warned: it’s a very knotty site… 
