Hello everyone,

I'm in need of some assistance with the following quesiton:

Let be collection of topological spaces and let be collection of subsets. Prove or bring a counter example showing whether:

in a) the product topology, b) the box topology.

I'm certain that it is incorrect in the product topology but I have yet to find a counter-example, as for the box topology I'm not sure.

I would greatly appreciate if someone could help me out here!

Thanks a lot.