K-analytic sets: Corrigenda et addenda. (English) Zbl 0557.54027
Summary: The authors give a revised form of the second part of Theorem 14 of their paper in the same journal 30, 189-211 (1983; Zbl 0524.54028): Let X be a completely regular space. If A can be expressed in the form \(G\cap S\), with G a paracompact set that is a \({\mathcal G}_{\delta}\)-set in \(\beta\) X, and with \(S\cap G\) a disjoint extended Souslin-\({\mathcal F}\) set in G, then A is a K-Lusin set in X. On the other hand, if A is a K-Lusin set in X, then A can be expressed in the form \(G\cap S\), with G a \({\mathcal G}_{\sigma}\)-set in \(\beta\) X, with S a Souslin-\({\mathcal F}\) set in \(\beta\) X, and with \(S\cap G\) a disjoint extended Souslin-\({\mathcal F}\) set in G.
MSC:
54H05 | Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) |
03E15 | Descriptive set theory |
Citations:
Zbl 0524.54028References:
[1] | DOI: 10.1112/plms/s3-28.4.683 · Zbl 0313.54044 · doi:10.1112/plms/s3-28.4.683 |
[2] | Hansell, Mathematika 30 pp 189– (1983) |
[3] | Engelking, General Topology (1977) |
[4] | Frolik, Bull. Acad. Pol., Sci. Sér. Math. 8 pp 747– (1960) |
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