Notes on monotonically metacompact generalized ordered spaces

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...

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Bibliographic Details
Published in:Open mathematics (Warsaw, Poland) Poland), 2015-02, Vol.13 (1)
Main Author: Xu, Ai-Jun
Format: Article
Language:English
Subjects:
Generalized ordered spaces
Monotonically countably metacompact
Monotonically metacompact
Online Access:Get full text
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Summary: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.
ISSN:2391-5455
2391-5455
DOI:10.1515/math-2015-0024