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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm185-3-6,
author = {Antonio Avil\'es},
title = {Weakly countably determined spaces of high complexity},
journal = {Studia Mathematica},
volume = {187},
year = {2008},
pages = {291-303},
zbl = {1144.46015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm185-3-6}
}
Antonio Avilés. Weakly countably determined spaces of high complexity. Studia Mathematica, Tome 187 (2008) pp. 291-303. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm185-3-6/