Monotone weak Lindelöfness

Maddalena Bonanzinga; Filippo Cammaroto; Bruno Pansera

Open Mathematics (2011)

  • Volume: 9, Issue: 3, page 583-592
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Maddalena Bonanzinga, Filippo Cammaroto, and Bruno Pansera. "Monotone weak Lindelöfness." Open Mathematics 9.3 (2011): 583-592. <http://eudml.org/doc/269415>.

@article{MaddalenaBonanzinga2011,
abstract = {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.},
author = {Maddalena Bonanzinga, Filippo Cammaroto, Bruno Pansera},
journal = {Open Mathematics},
keywords = {Monotone Lindelöfness; Weak Lindelöfness; Monotone weak Lindelöfness; monotonically weakly Lindelöf space; -base; Alexandroff duplicate; Sorgenfrey line},
language = {eng},
number = {3},
pages = {583-592},
title = {Monotone weak Lindelöfness},
url = {http://eudml.org/doc/269415},
volume = {9},
year = {2011},
}

TY - JOUR
AU - Maddalena Bonanzinga
AU - Filippo Cammaroto
AU - Bruno Pansera
TI - Monotone weak Lindelöfness
JO - Open Mathematics
PY - 2011
VL - 9
IS - 3
SP - 583
EP - 592
AB - 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.
LA - eng
KW - Monotone Lindelöfness; Weak Lindelöfness; Monotone weak Lindelöfness; monotonically weakly Lindelöf space; -base; Alexandroff duplicate; Sorgenfrey line
UR - http://eudml.org/doc/269415
ER -

References

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  12. [12] Levy R., Matveev M., Some more examples of monotonically Lindelöf and not monotonically Lindelöf spaces, Topology Appl., 2007, 154(11), 2333–2343 http://dx.doi.org/10.1016/j.topol.2007.04.002 Zbl1134.54006
  13. [13] Levy R., Matveev M., On monotone Lindelöfness of countable spaces, Comment. Math. Univ. Carolin., 2008, 49(1), 155–161 Zbl1212.54077
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