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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: 51–53, doi:10.1073/pnas.33.3.51, ISSN 0027-8424, JSTOR 87813, MR 0021239
Hazewinkel, Michiel, ed. (2001), "Eberlein compactum", Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4