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Monotone weak Lindelöfness

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Czasopismo
Rocznik
Tom
9
Numer
3
Strony
583-592
Opis fizyczny
Daty
wydano
2011-06-01
online
2011-03-22
Twórcy
Bibliografia
  • [1] Bennett H., Lutzer D., Matveev M., The monotone Lindelöf property and separability in ordered spaces, Topology Appl., 2005, 151(1–3), 180–186 http://dx.doi.org/10.1016/j.topol.2004.05.015
  • [2] Engelking R., General Topology, 2nd ed., Sigma Ser. Pure Math., 6, Heldermann, Berlin, 1989
  • [3] Frolik Z., Generalizations of compact and Lindelöf spaces, Czechoslovak Math. J., 1959, 9(84) (2), 172–217 (in Russian)
  • [4] Ge Y., Good C., A note on monotone countable paracompactness, Comment. Math. Univ. Carolin., 2001, 42(4), 771–778
  • [5] Good C., Haynes L., Monotone versions of countable paracompactness, Topology Appl., 2007, 154(3), 734–740 http://dx.doi.org/10.1016/j.topol.2006.08.006
  • [6] Good C., Knight R.W., Monotonically countably paracompact, collectionwise Hausdorff spaces and measurable cardinals, Proc. Amer. Math. Soc., 2006, 134(2), 591–597 http://dx.doi.org/10.1090/S0002-9939-05-07965-7
  • [7] Good C., Knight R., Stares I., Monotone countable paracompactness, Topology Appl., 2000, 101(3), 281–298 http://dx.doi.org/10.1016/S0166-8641(98)00128-X
  • [8] Gruenhage G., Generalized metric spaces, In: Handbook of the Set-Theoretic Topology, North-Holland, Amsterdam-New York-Oxford, 1984, 423–501
  • [9] Gruenhage G., Monotonically compact and monotonically Lindelöf spaces, Questions Answers Gen. Topology, 2008, 26(2), 121–130
  • [10] Gruenhage G., Monotonically compact T 2-spaces are metrizable, Questions Answers Gen. Topology, 2009, 27(1), 57–59
  • [11] Junnila H.J.K., Künzi H.-P.A., Ortho-bases and monotonic properties, Proc. Amer. Math. Soc., 1993, 119(4), 1335–1345 http://dx.doi.org/10.1090/S0002-9939-1993-1165056-6
  • [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
  • [13] Levy R., Matveev M., On monotone Lindelöfness of countable spaces, Comment. Math. Univ. Carolin., 2008, 49(1), 155–161
  • [14] Levy R., Matveev M., Some questions on monotone Lindelöfness, Questions Answers Gen. Topology, 2008, 26(1), 13–27
  • [15] Matveev M., A monotonically Lindelöf space need not be monotonically normal, 1994, preprint
  • [16] Pan C., Monotonically CP spaces, Questions Answers Gen. Topology, 1987, 15(1), 25–32
  • [17] Stares I.S., Versions of monotone paracompactness, In: Papers on General Topology and Applications, Gorham, August 10–13, 1995, Ann. N. Y. Acad Sci., 1996, 806, 433–438
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-011-0025-z
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