I. Juhász, Z. Szentmiklóssy and A. SzymanskiYakovlev showed that any Eberlein compactum is hereditarily -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.
Key words and phrases: Metrizability number, Eberlein compactum, separating family
2000 Mathematics Subject Classification: 54A38, 54A15