Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Reflecting Lindelöf and converging ω₁-sequences

100%

Dow A., Hart K.

Fundamenta Mathematicae

2014

tom 224

nr 3

205-218

We deal with a conjectured dichotomy for compact Hausdorff spaces: each such space contains a non-trivial converging ω-sequence or a non-trivial converging ω₁-sequence. We establish that this dichotomy holds in a variety of models; these include the Cohen models, the random real models and any model obtained from a model of CH by an iteration of property K posets. In fact in these models every compact Hausdorff space without non-trivial converging ω₁-sequences is first-countable and, in addition, has many ℵ₁-sized Lindelöf subspaces. As a corollary we find that in these models all compact Hausdorff spaces with a small diagonal are metrizable.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Dow A.

1 Hart K.

1 2014

Wyniki wyszukiwania

Reflecting Lindelöf and converging ω₁-sequences