Countable Compact Scattered T₂ Spaces and Weak Forms of AC

• Autorzy: Kyriakos Keremedis , Evangelos Felouzis , Eleftherios Tachtsis
• Języki publikacji: EN

Abstrakty

EN

We show that:
(1) It is provable in ZF (i.e., Zermelo-Fraenkel set theory minus the Axiom of Choice AC) that every compact scattered T₂ topological space is zero-dimensional.
(2) If every countable union of countable sets of reals is countable, then a countable compact T₂ space is scattered iff it is metrizable.
(3) If the real line ℝ can be expressed as a well-ordered union of well-orderable sets, then every countable compact zero-dimensional T₂ space is scattered.
(4) It is not provable in ZF+¬AC that there exists a countable compact T₂ space which is dense-in-itself.

Kategorie tematyczne

• 54E52: Baire category, Baire spaces
• 54E35: Metric spaces, metrizability
• 03E25: Axiom of choice and related propositions
• 54D30: Compactness
• 54D10: Lower separation axioms ( T 0 -- T 3 , etc.)
• 54A35: Consistency and independence results
• 54G12: Scattered spaces
• 03E35: Consistency and independence results
• 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: 2006
• Tom: 54
• Numer: 1
• Strony: 75-84

Daty

wydano

2006

Twórcy

autor

Kyriakos Keremedis

• Department of Mathematics, University of the Aegean, Karlovassi, 83 200, Samos, Greece

autor

Evangelos Felouzis

• Department of Mathematics, University of the Aegean, Karlovassi, 83 200, Samos, Greece

autor

Eleftherios Tachtsis

• Department of Statistics and, Actuarial-Financial Mathematics, University of the Aegean, Karlovassi, 83 200, Samos, Greece

Identyfikatory

DOI

10.4064/ba54-1-7