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A new countably determined Banach space. (English) Zbl 0537.46019

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.

MSC:

46B10 Duality and reflexivity in normed linear and Banach spaces
03E15 Descriptive set theory
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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
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