On Asplund spaces with the compact-open topology.

A famous theorem of Namioka and Phelps says that for a compact space , the Banach space is Asplund iff is scattered. We extend this result to the space of continuous real-valued functions endowed with the compact-open topology for several natural classes of non-compact Tychonoff spaces . The concept of -spaces recently introduced will be used for this research.