Let (an) be a sequence in X, (that is for al n in N, an in X) such that the set of the sequence, {an:n in N}, is infinite.

Using the definition of a convergence in topological spaces, prove that (an) has a subsequence which converges to p.

Note that X is an infinite and p a point in X chosen once and for all. Let T be the collection of subsets of V of Xfor which either p is NOT a member of V, or p in V, AND its compliment is finite.

A proof please?