Geodesic
Adequate Compacta which are Gul’ko or Talagrand
Serdica Mathematical Journal, Tome 29 (2003) no. 1, pp. 55-64

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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.
Keywords: 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 
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Čížek, Petr; Fabian, Marián. Adequate Compacta which are Gul’ko or Talagrand. Serdica Mathematical Journal, Tome 29 (2003) no. 1, pp. 55-64. http://geodesic.mathdoc.fr/item/SMJ2_2003_29_1_a4/