Sequential compactness vs. countable compactness

• Autorzy: Angelo Bella , Peter Nyikos
• Języki publikacji: EN

Abstrakty

EN

The general question of when a countably compact topological space is sequentially compact, or has a nontrivial convergent sequence, is studied from the viewpoint of basic cardinal invariants and small uncountable cardinals. It is shown that the small uncountable cardinal 𝔥 is both the least cardinality and the least net weight of a countably compact space that is not sequentially compact, and that it is also the least hereditary Lindelöf degree in most published models. Similar results, some definitive, are given for many other cardinal invariants. Special attention is paid to compact spaces. It is also shown that MA(ω₁) for σ-centered posets is equivalent to every countably compact T₁ space with an ω-in-countable base being second countable, and also to every compact T₁ space with such a base being sequential. No separation axioms are assumed unless explicitly stated.

Kategorie tematyczne

• 03E17: Cardinal characteristics of the continuum
• 54D30: Compactness
• 54D10: Lower separation axioms ( T 0 -- T 3 , etc.)
• 54A25: Cardinality properties (cardinal functions and inequalities, discrete subsets)
• 03E75: Applications of set theory
• 54D55: Sequential spaces
• 54B15: Quotient spaces, decompositions
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2010
• Tom: 120
• Numer: 2
• Strony: 165-189

Daty

wydano

2010

Twórcy

autor

Angelo Bella

• Dipartimento di Matematica, viale A. Doria 6, 95125 Catania, Italy

autor

Peter Nyikos

• Department of Mathematics, University of South Carolina, Columbia, SC 29208, U.S.A.

Identyfikatory

DOI

10.4064/cm120-2-1