Abstract:Yakovlev [{On bicompacta in $\Sigma $-products and related spaces}, Comment. Math. Univ. Carolin. {21.2} (1980), 263--283] showed that any Eberlein compactum is hereditarily $\sigma $-metacompact. We show that this property actually characterizes Eberlein compacta among compact spaces of finite metrizability number. Uniformly Eberlein compacta and Corson compacta of finite metrizability number can be characterized in an analogous way.
Keywords: metrizability number, Eberlein compactum, separating family
AMS Subject Classification: Primary 54A38, 54A15; Secondary A15