In mathematics an Eberlein compactum, studied by William Frederick Eberlein, is a compact topological space homeomorphic to a subset of a Banach space with the weak topology. Every compact metric space, more generally every one-point compactification of a locally compact metric space, is Eberlein compact. The converse is not true.

References

• 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]