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Asplund generated space; continuous image of Radon-Nikodym compact; totally disconnected compact; adequate compact; Eberlein compact
A family of compact spaces containing continuous images of Radon-Nikod'ym compacta is introduced and studied. A family of Banach spaces containing subspaces of Asplund generated (i.e., GSG) spaces is introduced and studied. Further, for a continuous image of a Radon-Nikod'ym compact $K$ we prove: If $K$ is totally disconnected, then it is Radon-Nikod'ym compact. If $K$ is adequate, then it is even Eberlein compact.
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