# Adequate Compacta which are Gul’ko or Talagrand

Serdica Mathematical Journal (2003)

- Volume: 29, Issue: 1, page 55-64
- ISSN: 1310-6600

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topČížek, 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 -

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