EDB — 2FD

[2FD]Prerequisites:[2F7]↺↻.Consider topological spaces \((X_ i,\tau _ i)\), each with the discrete topology (and each \(X_ i\) has at least two elements). Let \(I=ℕ\) or \(I=\{ 0,1,\ldots N\} \); let \(X=∏_{i∈ I} X_ i\) be the Cartesian product. We define the product topology \(𝜏\) on \(X\), as explained in [2F7]↺↻. Describe a simple base for this topology. Moreover, if \(I=ℕ\), show that the topology \(\tau \) is not the discrete topology.