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Eberlein compactum

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.

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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

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]