Small locally compact linearly Lindelöf spaces. (English) Zbl 1114.54015

Kunen, Kenneth

Topol. Proc. 29, No. 1, 193-198 (2005).

An example is constructed of a locally compact Hausdorff space of weight \(\aleph_{\omega}\) which is linearly Lindelöf and not Lindelöf. It is constructed by using a weak \(P_{\aleph_n}\) point, \(n \in \omega\), and an inverse limit. The example with ”\(\beth_{\omega}\)” replacing ”\(\aleph_{\omega}\)” was given by the same author [Commentat. Math. Univ. Carol. 43, No. 1, 155–158 (2002; Zbl 1090.54019)] as an answer to a question of A. V. Arhangel’skii and R. Z. Buzyakova.

Reviewer: Ken-ichi Tamano (Yokohama)

MSC:

54D20	Noncompact covering properties (paracompact, Lindelöf, etc.)
54D80	Special constructions of topological spaces (spaces of ultrafilters, etc.)
03E55	Large cardinals

Keywords:

Lindelöf; linearly Lindelöf; Jónsson cardinal; weak \(P\)-point

Citations:

Zbl 1090.54019