View More View Less
  • 1 Instituto de Matemática, Universidade Federal da Bahia, Campus de Ondina, Av. Adhemar de Barros, S/N, Ondina, CEP 40170-110 Salvador, BA, Brazil
Restricted access

Abstract

With a slight modification of a previous argument due to Schechter, we show that the Axiom of Choice is equivalent to the following topological statement: “If a product of a non-empty family of sets is closed in a topological (Tychonoff) product, then at least one of the factors is closed”. We also discuss the case on which one adds the hypothesis that the closed product of sets is a non-empty set.

  • [1] Bourbaki, N. 1939 Theorie des ensembles Éléments de mathématique Hermann Paris.

  • [2] Herrlich, H. 2006 Axiom of Choice Lecture Notes in Mathematics 1876 Springer-Verlag Berlin xiv + 194 pp.

  • [3] Howard, P., Rubin, J. E. 1998 Consequences of the Axiom of Choice Mathematical Surveys and Monographs 59 American Mathematical Society Providence RI viii + 432 pp.

    • Search Google Scholar
    • Export Citation
  • [4] de Jesus, J. P. C., Espacos métricos e topológicos na ausência do Axioma da Escolha (in Portuguese), MSc Dissertation, Federal University of Bahia (Salvador, Bahia, Brazil, 2010), 116 pp.

    • Search Google Scholar
    • Export Citation
  • [5] Schecther, E. 1992 Two topological equivalents of the Axiom of Choice Zeit. für Math. Logik und Grund. Math. 38 555557 .

Acta Mathematica Hungarica
P.O. Box 127
HU–1364 Budapest
Phone: (36 1) 483 8305
Fax: (36 1) 483 8333
E-mail: acta@renyi.mta.hu

  • Impact Factor (2019): 0.588
  • Scimago Journal Rank (2019): 0.489
  • SJR Hirsch-Index (2019): 38
  • SJR Quartile Score (2019): Q2 Mathematics (miscellaneous)
  • Impact Factor (2018): 0.538
  • Scimago Journal Rank (2018): 0.488
  • SJR Hirsch-Index (2018): 36
  • SJR Quartile Score (2018): Q2 Mathematics (miscellaneous)

For subscription options, please visit the website of Springer Nature

Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1950
Volumes
per Year
3
Issues
per Year
6
Founder Magyar Tudományos Akadémia
Founder's
Address
H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

Monthly Content Usage

Abstract Views Full Text Views PDF Downloads
Jan 2021 0 0 0
Feb 2021 0 0 0
Mar 2021 0 0 0
Apr 2021 0 0 0
May 2021 0 0 0
Jun 2021 0 0 0
Jul 2021 0 0 0