Abstract. We study the class of descriptive compact spaces, the Banach spaces generated by descriptive compact subsets and their relation to renorming problems.

Many classes of maps are characterized as (possibly multi-valued) maps preserving particular types of compact filters.

In this paper we characterize the classes of Gul'ko and Talagrand compact spaces through a network condition leading us to answer two questions posed by G. Gruenhage [Proc. Amer. Math. Soc. 100 (1987) 371-376] on covering properties.

No abstract

Abstract. We give a sufficient and necessary condition for a Radon-Nikodým compact space to be Eberlein compact in terms of a separable fibre connecting weak-* and norm approximation.