Notes on monotonically metacompact generalized ordered spaces

• Autorzy: Ai-Jun Xu
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Monotonically metacompact; Monotonically countably metacompact; Generalized ordered spaces

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2015
• Tom: 13
• Numer: 1

Daty

otrzymano

2014-02-28

zaakceptowano

2015-02-11

online

2015-02-27

Twórcy

autor

Ai-Jun Xu

• Department of Applied Mathematics, Nanjing Forest University, Nanjing 210037, PR China

Bibliografia

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

Identyfikatory

DOI

10.1515/math-2015-0024