I’ve figured out the difference, I was using the box topology https://en.wikipedia.org/wiki/Box_topology , while you were using the https://en.wikipedia.org/wiki/Product_topology.
You are correct. I knew about finite topological products and made a natural generalization, but it turns out not to be the standard meaning of Iw.
Thanks for introducing me to the box topology—seeing it defined so explicitly, and seeing what properties it fails, cleared up a few of my intuitions.
I’ve figured out the difference, I was using the box topology https://en.wikipedia.org/wiki/Box_topology , while you were using the https://en.wikipedia.org/wiki/Product_topology.
You are correct. I knew about finite topological products and made a natural generalization, but it turns out not to be the standard meaning of Iw.
Thanks for introducing me to the box topology—seeing it defined so explicitly, and seeing what properties it fails, cleared up a few of my intuitions.