There is a locally compact Hausdorff space which is linearly Lindelöf and not Lindelöf. This answers a question of Arhangel'skii and Buzyakova.
@article{119307, author = {Kenneth Kunen}, title = {Locally compact linearly Lindel\"of spaces}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {43}, year = {2002}, pages = {155-158}, zbl = {1090.54019}, mrnumber = {1903314}, language = {en}, url = {http://dml.mathdoc.fr/item/119307} }
Kunen, Kenneth. Locally compact linearly Lindelöf spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) pp. 155-158. http://gdmltest.u-ga.fr/item/119307/
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