A topological space is hereditarily Lindelof if every collection of open sets in the space contains a countable subcollection with the same union. It is difficult to construct ZFC example of such spaces which are nonseparable. Recently Yinhe Peng and Liuzhen Wu constructed an example of such
a space which is also a topological group. In fact their example has the property that its square is non Lindelof, solving an old problem of Arhangelskii. They also construct, for each n, a topological space X such that X^n is hereditarily Lindelof and non separable but such that X^(n+1) contains an uncountable discrete subspace.