Productively Lindelof and Indestructibly Lindelof Spaces

There has recently been considerable interest in productively Lindelof spaces, i.e. spaces such that their product with every Lindelof space is Lindelof. Here we make several related remarks about such spaces. Indestructible Lindelof spaces, i.e. spaces that remain Lindelof in every countably closed forcing extension, were introduced by Tall in 1995. Their connection with topological games and selection principles was explored by Scheepers and Tall in 2010. We find further connections here.