Fill the table below,  justifying your answers. (For instance, the finite product of compact spaces is compact, by Theorem 26.7. Hence in the cell "compact" and
finite product", we can write true.) The topology in all cases is the product topology.
I already filled some cells but you need to find counterexamples or justifications for all cases.

Property of factor spaces	Finite product	Countable product	Uncountable product
Compact
Sequencially compact
Locally compact	True	False
Lindelof	False (Hint: take a product RxR,  but of course, you need to topologize R with a topology that is not the standard)