Adequate Compacta which are Gul’ko or Talagrand
2000 Mathematics Subject Classification: 54H05, 03E15, 46B26 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. Supported by grants AV CR 101-90-03, and GA CR 201-01-1198...