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Can one define a function that sends lets say a line in r2 to a volume in r3?

  1. Mar 9, 2012 #1
    Or perhaps there is a more general function that sends to the next hypervolume? Can it be bijective? Continuous?
     
  2. jcsd
  3. Mar 9, 2012 #2
  4. Mar 9, 2012 #3
    Ah ^thanks, so by this logic we can define H(x,y)--> (h(x),h(y),h(yx),h(xy),h(xx),h(yy)...)?

    thus we can go from R^2-->R^n?
     
  5. Mar 9, 2012 #4

    mathwonk

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    it can either be bijective or be continuous but not both, I think.
     
  6. Mar 13, 2012 #5

    Bacle2

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    Maybe you're referring to mapping a (closed) line segment? In that case, you would have a bijection between compact and Hausdorff, which is a homeomorphism?

    To the OP: I'm curious: why are you considering a line embedded in ℝ2, instead of considering ℝ itself?
     
  7. Mar 13, 2012 #6

    Bacle2

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  8. Mar 13, 2012 #7

    Bacle2

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  9. Mar 13, 2012 #8

    Bacle2

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