Talagrand Compact Gul’ko Compact K−Analytic Space K−Countably Determined Space Analytic Set Coanalytic Set Adequate Family ill-Founded Tree Well-Founded Tree Mercourakis Space
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 29, No 1, (2003), 55p-64p
We answer positively a question raised by S. Argyros: Given
any coanalytic, nonalytic subset Σ′ of the irrationals, we construct, in Mercourakis space c1(Σ′), an adequate compact which is Gul’ko and not Talagrand. Further, given any Borel, non Fσ subset Σ′ of the irrationals, we construct, in c1(Σ′), an adequate compact which is Talagrand and not Eberlein.