On the compactness and countable compactness of 2R in ZF

• Autorzy: Keremedis K. , Felouzis E. , Tachtsis E.
• Języki publikacji: EN

Abstrakty

EN

In the framework of ZF (Zermelo-Fraenkel set theory without the Axiom of Choice) we provide topological and Boolean-algebraic characterizations of the statements "2R is countably compact" and "2R is compact".

Słowa kluczowe

EN

axiom of choice; weak axioms of choice; Tychonoff products; compact spaces; countably compact spaces; Lindelof spaces; Boolean algebras; filters; ultrafilters

PL

aksjomat wyboru; przestrzeń zwarta; przestrzeń Lindelofa; algebra Boole'a; filtr; ultrafiltr

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2007
• Tom: Vol. 55, no 4
• Strony: 293--302
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Keremedis K.

autor

Felouzis E.

autor

Tachtsis E.

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

Bibliografia

• [1] P. Howard and J. E. Rubin, Consequences of the Axiom of Choice, Math. Surveys Monogr. 59, Amer. Math. Soc., 1998.
• [2] T. Jech, The Axiom of Choice, North-Holland, Amsterdam, 1973.
• [3] K. Keremedis, The compactness of 2R and some weak forms of the axiom of choice, Math. Logic Quart. 46 (2000), 569-571.
• [4] —, Tychonoff products of two-element sets and some weakenings of the Boolean prime ideal theorem, Bull. Polish Acad. Sci. Math. 53 (2005), 349-359.
• [5] S. Willard, General Topology, Addison-Wesley, 1968.