The box topology on R^ω

1. Nov 14, 2014

hedipaldi

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

2. Nov 16, 2014

Stephen Tashi

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. Nov 16, 2014

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)