> On Sunday, November 11, 2012 5:09:34 PM UTC+8, William Elliot wrote: > > ...Do you mean the topological closure or some algebra construction? > > > How are you defining lim(n->oo) X_n?
> "Strong convergence" ("convergence in the norm"); that is, the norm > induced by the inner product:
> For any e>0 there exists N such that > || x-x_n || < e for all n>N > That's the usual definition for a sequence of points to converge to a point. It has nothing to do with a sequence of subsets or subspaces converging to a set or subspace. How for example, are you defining ||X - X_n|| for sets X and X_n?