Compactness of Powers of ω

• Autorzy: Paolo Lipparini
• Języki publikacji: EN

Abstrakty

EN

We characterize exactly the compactness properties of the product of κ copies of the space ω with the discrete topology. The characterization involves uniform ultrafilters, infinitary languages, and the existence of nonstandard elements in elementary extensions. We also have results involving products of possibly uncountable regular cardinals.

Kategorie tematyczne

• 03C20: Ultraproducts and related constructions
• 03E05: Other combinatorial set theory
• 03C75: Other infinitary logic
• 54B10: Product spaces
• 54A20: Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)
• 54A25: Cardinality properties (cardinal functions and inequalities, discrete subsets)
• 54D20: Noncompact covering properties (paracompact, Lindel\"of, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2013
• Tom: 61
• Numer: 3
• Strony: 239-246

Daty

wydano

2013

Twórcy

autor

Paolo Lipparini

• Dipartimento di Matematica, II Università di Roma (Tor Vergata), Viale della Ricerca Scientifica, I-00133 Roma, Italy

Identyfikatory

DOI

10.4064/ba61-3-5