Network characterization of Gul’ko compact spaces and their relatives ✩

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.  2004 Elsevier Inc. All rights reserved.