In mathematics an Eberlein compactum, studied by
William Frederick Eberlein, is a
compact topological space
In mathematics, a topological space is, roughly speaking, a Geometry, geometrical space in which Closeness (mathematics), closeness is defined but cannot necessarily be measured by a numeric Distance (mathematics), distance. More specifically, a to ...
homeomorphic to a subset of a
Banach space
In mathematics, more specifically in functional analysis, a Banach space (, ) is a complete normed vector space. Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vectors and ...
with the
weak topology.
Every compact
metric space
In mathematics, a metric space is a Set (mathematics), set together with a notion of ''distance'' between its Element (mathematics), elements, usually called point (geometry), points. The distance is measured by a function (mathematics), functi ...
, more generally every
one-point compactification of a
locally compact metric space, is Eberlein compact. The converse is not true.
References
*
*{{eom, id=Eberlein_compactum, title=Eberlein compactum
General topology