We consider the families of all subspaces of size ω₁ of (or of a compact zero-dimensional space X of weight ω₁ in general) which are normal, have the Lindelöf property or are closed under limits of convergent ω₁-sequences. Various relations among these families modulo the club filter in are shown to be consistently possible. One of the main tools is dealing with a subspace of the form X ∩ M for an elementary submodel M of size ω₁. Various results with this flavor are obtained. Another tool used is forcing and in this case various preservation or nonpreservation results of topological and combinatorial properties are proved. In particular we prove that there may be no c.c.c. forcing which destroys the Lindelöf property of compact spaces, answering a question of Juhász. Many related questions are formulated.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm169-3-2,
author = {L\'ucia Junqueira and Piotr Koszmider},
title = {On families of Lindelof and related subspaces of $2^{o1}$
},
journal = {Fundamenta Mathematicae},
volume = {167},
year = {2001},
pages = {205-231},
zbl = {0984.03040},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm169-3-2}
}
Lúcia Junqueira; Piotr Koszmider. On families of Lindelöf and related subspaces of $2^{ω₁}$
. Fundamenta Mathematicae, Tome 167 (2001) pp. 205-231. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm169-3-2/