Reflecting Lindelöf and converging ω₁-sequences

Alan Dow, and Klaas Pieter Hart. "Reflecting Lindelöf and converging ω₁-sequences." Fundamenta Mathematicae 224.3 (2014): 205-218. <http://eudml.org/doc/283349>.

@article{AlanDow2014,
abstract = {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.},
author = {Alan Dow, Klaas Pieter Hart},
journal = {Fundamenta Mathematicae},
keywords = {compact space; first-countable space; lindelöfness; converging sequence; L-reflection; small diagonal; forcing; property K},
language = {eng},
number = {3},
pages = {205-218},
title = {Reflecting Lindelöf and converging ω₁-sequences},
url = {http://eudml.org/doc/283349},
volume = {224},
year = {2014},
}

TY - JOUR
AU - Alan Dow
AU - Klaas Pieter Hart
TI - Reflecting Lindelöf and converging ω₁-sequences
JO - Fundamenta Mathematicae
PY - 2014
VL - 224
IS - 3
SP - 205
EP - 218
AB - 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.
LA - eng
KW - compact space; first-countable space; lindelöfness; converging sequence; L-reflection; small diagonal; forcing; property K
UR - http://eudml.org/doc/283349
ER -