Convergence Criteria for Box Topology on R^ω

[hedipaldi]

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

 

[Stephen Tashi]

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?

 

[hedipaldi]

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)