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Keywords:
metrizability number; Eberlein compactum; separating family
metrizability number; Eberlein compactum; separating family
Summary:
Yakovlev [{\it On bicompacta in $\Sigma $-products and related spaces\/}, Comment. Math. Univ. Carolin. {\bf 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.
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