Spaces with large weak extent

In this paper, we show the following statements:(1)For any cardinal κ, there exists a pseudocompact centered-Lindelöf Tychonoff space X such that we(X)⩾κ.(2)Assuming ℵ02=ℵ12, there exists a centered-Lindelöf normal space X such that we(X)⩾ω1.