The shrinking property and the B-property in ordered spaces
Nobuyuki Kemoto (1990)
Fundamenta Mathematicae
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Nobuyuki Kemoto (1990)
Fundamenta Mathematicae
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Harold Bennett, David Lutzer (1980)
Fundamenta Mathematicae
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Witold Bula (1984)
Fundamenta Mathematicae
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Harold Bennett, William Fleissner, David Lutzer (1981)
Fundamenta Mathematicae
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Norman Howes (1980)
Fundamenta Mathematicae
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Teodor Przymusiński (1981)
Fundamenta Mathematicae
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Ai-Jun Xu (2015)
Open Mathematics
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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.
Teodor Przymusiński (1976)
Fundamenta Mathematicae
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P. Nyikos, H. Reichel (1976)
Fundamenta Mathematicae
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Harold Bennett, David Lutzer (2013)
Fundamenta Mathematicae
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We examine the Gruenhage property, property * (introduced by Orihuela, Smith, and Troyanski), fragmentability, and the existence of σ-isolated networks in the context of linearly ordered topological spaces (LOTS), generalized ordered spaces (GO-spaces), and monotonically normal spaces. We show that any monotonically normal space with property * or with a σ-isolated network must be hereditarily paracompact, so that property * and the Gruenhage property are equivalent in monotonically...