Spaces with large weak extent

摘要

In this paper, we show the following statements: (1) For any cardinal k, there exists a pseudocompact centered-Lindelbf Tychonoff space X such that we(X) ≥k. (2) Assuming 2(Ψ_0)= 2~(s_1), there exists a centered-Lindeloef normal space X such that we(X) ≥ ω_1.