The class of Eberlein compacts (those compacts spaces homeomorphic to a weakly compact subset of a Banach space) is well known and well studied; one of the many properties it enjoys is that every set in this class is also sequentially compact, thanks to Eberlein-Smulian.
This led me to wonder: Eberlein-Smulian also holds in greater generality than for Banach spaces (as long as the Mackey topology in the space in question is quasicomplete, for example, the result holds). What is then known about the class of compact spaces that are homeomorphic to a weakly compact subset of, say, a Mackey quasicomplete space? Does it coincide with the class of Eberlein compacta?