Remarks on the Stone Spaces of the Integers and the Reals without AC

• Autorzy: Horst Herrlich , Kyriakos Keremedis , Eleftherios Tachtsis
• Języki publikacji: EN

Abstrakty

EN

In ZF, i.e., the Zermelo-Fraenkel set theory minus the Axiom of Choice AC, we investigate the relationship between the Tychonoff product $2^{𝓟(X)}$, where 2 is 2 = {0,1} with the discrete topology, and the Stone space S(X) of the Boolean algebra of all subsets of X, where X = ω,ℝ. We also study the possible placement of well-known topological statements which concern the cited spaces in the hierarchy of weak choice principles.

Kategorie tematyczne

• 03E25: Axiom of choice and related propositions
• 54D30: Compactness
• 54B10: Product spaces
• 54D80: Special constructions of spaces (spaces of ultrafilters, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2011
• Tom: 59
• Numer: 2
• Strony: 101-114

Daty

wydano

2011

Twórcy

autor

Horst Herrlich

• Feldhäuser Str. 69, 28865 Lilienthal, Germany

autor

Kyriakos Keremedis

• Department of Mathematics, University of the Aegean, Karlovassi, Samos 83200, Greece

autor

Eleftherios Tachtsis

• Department of Statistics and Actuarial-Financial Mathematics, University of the Aegean, Karlovassi, Samos 83200, Greece

Identyfikatory

DOI

10.4064/ba59-2-1