Adequate families of sets and function spaces

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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.
Original languageEnglish
Pages (from-to)31-39
Number of pages9
JournalCommentationes Mathematicae Universitatis Carolinae
Issue number1
StatePublished - 1988


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