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.
- 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, ISSN 0027-8424, JSTOR 87813, MR 0021239
- Hazewinkel, Michiel, ed. (2001), "Eberlein compactum", Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4