Rosenthal compact

Definition

• Let K be a compact Hausdorff space. K is a Rosenthal compact iff K is homeomorphic to a pointwise compact set of functions of first Baire class on a Polish space.

Property

• The product of two Rosenthal compacts is a Rosenthal compact.
• Every compact metric space is Rosenthal compact.

Reference

• Edgar, G. A. and Wheeler, R. F. , Topological properties of Banach spaces, Pacific J. Math. 115 (1984), no. 2, 317--350.