angelic compact

Definition

• Let K be a compact Hausdorff space. K is an angelic compact (also called a compact Frechet space) iff the closure of every subset A is the set of limits of sequences from A.

Property

• Every compact metric space is both Eberlein compact and Rosenthal compact, and each of these is angelic.
• If K is an Eberlein compact and L is a Rosenthal compact, then K×L is angelic.

Reference

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