Notes on monotonically metacompact generalized ordered spaces

Ai-Jun Xu

Open Mathematics (2015)

  • Volume: 13, Issue: 1
  • ISSN: 2391-5455

Abstract

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In this paper, we show that any generalized ordered space X is monotonically (countably) metacompact if and only if the subspace X - { x } is monotonically (countably) metacompact for every point x of X and monotone (countable) metacompact property is hereditary with respect to convex (open) subsets in generalized ordered spaces. In addition, we show the equivalence of two questions posed by H.R. Bennett, K.P. Hart and D.J. Lutzer.

How to cite

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Ai-Jun Xu. "Notes on monotonically metacompact generalized ordered spaces." Open Mathematics 13.1 (2015): null. <http://eudml.org/doc/270002>.

@article{Ai2015,
abstract = {In this paper, we show that any generalized ordered space X is monotonically (countably) metacompact if and only if the subspace X - \{ x \} is monotonically (countably) metacompact for every point x of X and monotone (countable) metacompact property is hereditary with respect to convex (open) subsets in generalized ordered spaces. In addition, we show the equivalence of two questions posed by H.R. Bennett, K.P. Hart and D.J. Lutzer.},
author = {Ai-Jun Xu},
journal = {Open Mathematics},
keywords = {Monotonically metacompact; Monotonically countably metacompact; Generalized ordered spaces},
language = {eng},
number = {1},
pages = {null},
title = {Notes on monotonically metacompact generalized ordered spaces},
url = {http://eudml.org/doc/270002},
volume = {13},
year = {2015},
}

TY - JOUR
AU - Ai-Jun Xu
TI - Notes on monotonically metacompact generalized ordered spaces
JO - Open Mathematics
PY - 2015
VL - 13
IS - 1
SP - null
AB - In this paper, we show that any generalized ordered space X is monotonically (countably) metacompact if and only if the subspace X - { x } is monotonically (countably) metacompact for every point x of X and monotone (countable) metacompact property is hereditary with respect to convex (open) subsets in generalized ordered spaces. In addition, we show the equivalence of two questions posed by H.R. Bennett, K.P. Hart and D.J. Lutzer.
LA - eng
KW - Monotonically metacompact; Monotonically countably metacompact; Generalized ordered spaces
UR - http://eudml.org/doc/270002
ER -

References

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  1. [1] Bennett H.R., Hart K.P., Lutzer D.J., A note on monotonically metacompact spaces, Topology Appl., 2010, 157, 456-465 [WoS] Zbl1184.54023
  2. [2] Engleking R., General Topology, 2nd ed., Sigma Ser. Pure Math., 6, Hedermann, Berlin, 1989 
  3. [3] Kemoto N., Normality of Products of GO-spaces and cardinals, Topology Proc., 1993, 18, 133-142 Zbl0832.54029
  4. [4] Lutzer D.J., Ordered topological spaces, In: Surveys in General Topology, Reed G.M., Academic Press, New York, 1980, 247-296 
  5. [5] Popvassilev S.G., !1 C1 is not monotonically countably compact, Questions Answers Gen. Topology, 2009, 27, 133-135 Zbl1182.54028
  6. [6] Xu A.J., Shi W.X., Notes on monotone Lindelöf property, Czechoslovak Math. J., 2009, 59, 943-955 Zbl1224.54073
  7. [7] Xu A.J., Shi W.X., Monotone Lindelöf property and linearly ordered extensions, Bull. Aust. Math. Soc., 2010, 81, 418-424 Zbl1190.54023
  8. [8] Xu A.J., Shi W.X., A result on monotonically metacompact spaces, Houston J. Math., 2013, 39, 1437-1442 Zbl1282.54018

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