Adequate Compacta Which Are Gul’ko or Talagrand

Abstract

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. 0. Introduction. On the last Sunday of August 1998, the first named author, Petr Čı́žek died at a car accident in the U.S.A. This paper was prepared on the basis of his Diploma Thesis [2] by the second named author, his supervisor. 2000 Mathematics Subject Classification: 54H05, 03E15, 46B26

Cite this paper

@inproceedings{ek2009AdequateCW, title={Adequate Compacta Which Are Gul’ko or Talagrand}, author={Petr {\vC}́ı{\vz}ek and Mari{\'a}n Fabian and Jan Pelant and Petr {\vC}ı́{\vz}ek}, year={2009} }