I'm reading through a book and have come across something that seems like an obvious error to me. The books says

Now it's been a long time since I've done any topology, but isn't this the box topology rather than the product topology? I just want to make sure I'm not going crazy.

I think the product topology and box topology coincide for finite products. If you are looking at the space X x Y in particular, then the product topology is generated by the set