Small Locally Compact Linearly Lindelof Spaces

TL;DR

This paper constructs a specific locally compact Hausdorff space of weight aleph_omega that is linearly Lindelof but not Lindelof, improving previous results on the subject.

Contribution

It presents a new example of a locally compact space with a smaller weight that is linearly Lindelof but not Lindelof, refining earlier constructions.

Findings

Constructed a space of weight aleph_omega with the desired properties.

Improved the known bounds from beth_omega to aleph_omega.

Demonstrated the existence of such a space within the specified conditions.

Abstract

There is a locally compact Hausdorff space of weight aleph_omega which is linearly Lindelof and not Lindelof. This improves an earlier result, which produced such a space of weight beth_omega.