Problem 13. Show that (No, T) is homeomorphic to A = {1/n | ne

N} U {0} with the subspace topology from R.

Let (No XNoo, Tprod) be the product of two copies of (Noo, Jo). Given a

function g: Nox No → X, let m,n = g(m, n) for m, n E No, and consider

the sequences (m,n)neN in X, one for each me N, and the sequences

(m,n)meN in X, one for each n € No.