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Sequential compactness vs. countable compactness

100%

Bella A., Nyikos P.

Colloquium Mathematicum

2010

tom 120

nr 2

165-189

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.

Sequential + separable vs sequentially separable and another variation on selective separability

81%

Bella A., Bonanzinga M., Matveev M.

Open Mathematics

2013

tom 11

nr 3

530-538

A space X is sequentially separable if there is a countable D ⊂ X such that every point of X is the limit of a sequence of points from D. Neither “sequential + separable” nor “sequentially separable” implies the other. Some examples of this are presented and some conditions under which one of the two implies the other are discussed. A selective version of sequential separability is also considered.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Open Mathematics

2 Bella A.

1 Bonanzinga M.

1 Matveev M.

1 Nyikos P.

1 2013

1 2010

Wyniki wyszukiwania

Sequential compactness vs. countable compactness

Sequential + separable vs sequentially separable and another variation on selective separability