Talagrand, Michel A new countably determined Banach space. (English) Zbl 0537.46019 Isr. J. Math. 47, 75-80 (1984). We construct a compact space K with the following properties. The Banach space \(X=C(K)\), provided with the weak topology, is an upper-continuous compact valued image of a separable metric space, but is not an upper- continuous compact valued image of the irrational. In other words, X is countably determined, but is not K-analytic. The technique of construction of K has subsequently proved useful in constructing other types of compacts. Cited in 3 ReviewsCited in 21 Documents MSC: 46B10 Duality and reflexivity in normed linear and Banach spaces 03E15 Descriptive set theory Keywords:WCG space; upper-continuous compact valued image of a separable metric space; countably determined; K-analytic PDFBibTeX XMLCite \textit{M. Talagrand}, Isr. J. Math. 47, 75--80 (1984; Zbl 0537.46019) Full Text: DOI References: [1] Choquet, G., Lectures on Analysis (1969), New York: W. A. Benjamin, Inc., New York · Zbl 0181.39601 [2] Frolick, Z., A survey of separable descriptive theory of sets and spaces, Czech. Math. J., 20, 406-467 (1970) · Zbl 0223.54028 [3] K. Kuratowski,Topologie, Warsawa, 1933. [4] Talagrand, M., Espaces de Banach faiblement K-analytiques, Ann. of Math., 110, 407-438 (1979) · Zbl 0393.46019 · doi:10.2307/1971232 [5] Vasak, L., On a generalisation of weakly compactly generated Banach spaces, Studia Math., 70, 11-19 (1981) · Zbl 0376.46012 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.