The definition of monotone weak Lindelöfness is similar to monotone versions of other covering properties: X is monotonically weakly Lindelöf if there is an operator r that assigns to every open cover U a family of open sets r(U) so that (1) ∪r(U) is dense in X, (2) r(U) refines U, and (3) r(U) refines r(V) whenever U refines V. Some examples and counterexamples of monotonically weakly Lindelöf spaces are given and some basic properties such as the behavior with respect to products and subspaces are discussed.
@article{bwmeta1.element.doi-10_2478_s11533-011-0025-z,
author = {Maddalena Bonanzinga and Filippo Cammaroto and Bruno Pansera},
title = {Monotone weak Lindel\"ofness},
journal = {Open Mathematics},
volume = {9},
year = {2011},
pages = {583-592},
zbl = {1237.54020},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0025-z}
}
Maddalena Bonanzinga; Filippo Cammaroto; Bruno Pansera. Monotone weak Lindelöfness. Open Mathematics, Tome 9 (2011) pp. 583-592. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0025-z/
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