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Topology question?

  1. Apr 1, 2005 #1
    I read how in topology you can bend a ractangle into a cylinder and then the cylinder into a torus. I'm a beginner to topology, so how is the torus described topologically? Is it just a set of all points? or an equation?
     
  2. jcsd
  3. Apr 2, 2005 #2

    matt grime

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    How are those different? That is the basis of algebraic geometry.

    There are several ways ot model a torus.

    There is the "flat" torus, which is the set of all points in R^2 modulo the relation (x,y)~(u,v) iff x-u and y-v are integers, with the quotient topology.

    Then there is the "complex" torus which is the product of two circles of radius 1: S^1xS^1 with the product toplogy on it, adn the natural subspace topologyon S^1 thought of as a subset of C (or R^2). This is a subspace of C^2 or R^4 and the topology is also the same as the subspace topology.

    These are all homeomorphic.
     
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