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The box topology on R^ω

  1. Nov 14, 2014 #1
    What are the convergent sequences in the box topology on R^ω?Are they the eventually constant only?
    Thank's in advance
  2. jcsd
  3. Nov 16, 2014 #2

    Stephen Tashi

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    Science Advisor

    Does "eventually constant" refer to a limiting sequence that itself converges to some constant value? Or does it refer to a limiting sequence whose terms eventually all become a constant value, like 1,2,....5,5,5,5....? - or perhaps to a sequence, each of whose terms is the same constant value?
  4. Nov 16, 2014 #3
    I am trying to show tha the coorinates Xn,m=X0,m for n and m greater from som M and N.(where Xn converges to X0 in the box topology)
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