Adequate Compacta which are Gul’ko or Talagrand

Čížek, Petr, and Fabian, Marián. "Adequate Compacta which are Gul’ko or Talagrand." Serdica Mathematical Journal 29.1 (2003): 55-64. <http://eudml.org/doc/219629>.

@article{Čížek2003,
abstract = {2000 Mathematics Subject Classification: 54H05, 03E15, 46B26We 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},
author = {Čížek, Petr, Fabian, Marián},
journal = {Serdica Mathematical Journal},
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},
language = {eng},
number = {1},
pages = {55-64},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Adequate Compacta which are Gul’ko or Talagrand},
url = {http://eudml.org/doc/219629},
volume = {29},
year = {2003},
}

TY - JOUR
AU - Čížek, Petr
AU - Fabian, Marián
TI - Adequate Compacta which are Gul’ko or Talagrand
JO - Serdica Mathematical Journal
PY - 2003
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 29
IS - 1
SP - 55
EP - 64
AB - 2000 Mathematics Subject Classification: 54H05, 03E15, 46B26We 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
LA - eng
KW - 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
UR - http://eudml.org/doc/219629
ER -