In mathematics anEberlein compactum, studied byWilliam Frederick Eberlein, is acompacttopological spacehomeomorphic to a subset of aBanach space with theweak topology.Every compactmetric space, more generally everyone-point compactification of alocally compact metric space, is Eberlein compact. The converse is not true.

• Eberlein, W. F. (1947), "Weak compactness in Banach spaces. I",Proceedings of the National Academy of Sciences of the United States of America,33 (3):51–53,Bibcode:1947PNAS...33...51E,doi:10.1073/pnas.33.3.51,ISSN 0027-8424,JSTOR 87813,MR 0021239,PMC 1078986,PMID 16578243
• "Eberlein compactum",Encyclopedia of Mathematics,EMS Press, 2001 [1994]

• General topology