Adequate families of sets and function spaces

Let X be an Eberlein-Grothendieck s space possessing the only one nonisolated point. In this paper we show that the space X is completely described in terms of adequate families of sets. As an application it is prdved that for this space X the space C (X) is K-analytic (a Lindelbf 2E-space) iff X satisfies some property (A ) (is a Lindelbf 2E-space). Other applications concerning the space C (K), where K is a Corson compact, are obtained.