The box topology on R^ω

  • Thread starter hedipaldi
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  • #1
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Hi,
What are the convergent sequences in the box topology on R^ω?Are they the eventually constant only?
Thank's in advance
 

Answers and Replies

  • #2
Stephen Tashi
Science Advisor
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Are they the eventually constant only?

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?
 
  • #3
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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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