Quote:

Let B be the collection of subsets of R in the form [a,b) for all a < b, the empty set, and the whole set included.

Let T be the topology on R determined by taking all arbitrary unions of sets in B. Show the sequence {1+ (1/n), n= 1,2, ...} converges to one in the topology T.

I thought it was obvious that this sequence converges to 1 because 1/n converges to 0, but then I got confused by the next part.

Show that the sequence {1 - (1/n), n=1,2,...} does NOT converge to 1 in the topology T. I'm assuming this may have something to do with [a,b) where b is not included, but I"m not sure.

No, it has to do with the definition of convergence in a topology (Wink)