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if so can you see that, from the point of view of continuity, a circle and a line are different, but a circle and a square are the same? and a line and a half circle are the same?

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ya topology is also nicknamed "rubber-sheet geometry" because if you imagine everything as being made out of rubber you could stretch/compress it into other shapes "homeomorphic" (similar-shape) to the one you start with. a topologist is someone who can't tell the difference between a doughnut & a coffee cup

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we have something like this, and it's called "sufgania" (this is how you pronounce it in hebrew), but it's too much fattening, beware!!! :surprisedmatt grime said:

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No, then we are topologically equivalent to a DOUBLE torus.Sirus said:Similarly, a human is topologically equivalent to a torus when he plugs his nose.

(You've forgotten the big chute connecting your (open) mouth and ass)

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That reminds me of a picture and a small discussion in "A Brief History of Time" by Hawking.He gave a reasonable explanation why a dog could not exist in 2 dimensions :tongue2: .I believe it could be said for every living organism with a digestive tractum.arildno said:No, then we are topologically equivalent to a DOUBLE torus.

(You've forgotten the big chute connecting your (open) mouth and ass)

Daniel.

Why couldn't a dog exist in 2d ?dextercioby said:That reminds me of a picture and a small discussion in "A Brief History of Time" by Hawking.He gave a reasonable explanation why a dog could not exist in 2 dimensions :tongue2: .I believe it could be said for every living organism with a digestive tractum.

Daniel.

it just so happens we live in 3d ? nobody knows why ?

roger

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Daniel.

topology has already begun to appear in the definition of continuity, if one has the concept of a "neighborhood" in the definition. i.e. a neighborhood of a point p, is a set of reals which contains an interval of form (p-e,p+e), for some positive e. then a function defined on the reals is continuous at p, if for every neighborhood V of f(p), there is a neighborhood U of p, such that f(U) is contained in V. This definition of continuity uses only topological properties.

once we have continuity we can define homeomorphism. i.e. two sets are homeomorphic if there are mutually inverse mappings between them, both continuous. then topology is the study of properties which are the same for any two homeomorphic sets. for example in the reals, a set S is homeomorphic to an open interval T if and only if S is also an open interval.

I don't understand. A torus has one hole in it. If you plug your nose, the only hole in your body is this very 'chute' you speak of. To be a double torus, there would have to be two holes. What is the other hole?arildno said:No, then we are topologically equivalent to a DOUBLE torus.

(You've forgotten the big chute connecting your (open) mouth and ass)

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your arm is a handle isn't it? it would be attached to your shoulder at 1 end, & your nose at the other end, and that makes a handle. so there's one hole between your arm & body, and that other holeSirus said:I don't understand. A torus has one hole in it. If you plug your nose, the only hole in your body is this very 'chute' you speak of. To be a double torus, there would have to be two holes. What is the other hole?

Wow...missed that. I think the topological human becomes more complicated considering that there are two 'exits' in the digestive tract. Not sure what that makes then.fourier jr said:your arm is a handle isn't it? it would be attached to your shoulder at 1 end, & your nose at the other end, and that makes a handle. so there's one hole between your arm & body, and that other hole

Anyways, I think we have sufficiently answered the original poster's question.

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but are both exits connected directly to entrance?

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