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

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.

### MSC:

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

Zbl 1090.54019
Full Text: