Weakly countably determined spaces of high complexity

Details Weakly countably determined spaces of high complexity Weakly countably determined spaces of high complexity

2009-03-04

arxiv.org/abs/0903.0852v1

Stud. Math. 185, No. 3, 291-303 (2008)

Mathematics

Functional Analysis

This version differs from the published in Studia Mathematica in that there is a short correction to a mistake discovered by t

Scientific paper

We prove that there exist weakly countably determined spaces of complexity
higher than coanalytic. On the other hand, we also show that coanalytic sets
can be characterized by the existence of a cofinal adequate family of closed
sets. Therefore the Banach spaces constructed by means of these families have
at most coanalytic complexity.

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