Displaying similar documents to “The Gruenhage property, property *, fragmentability, and σ-isolated networks in generalized ordered spaces”

Notes on monotonically metacompact generalized ordered spaces

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.

Calibres, compacta and diagonals

Paul Gartside, Jeremiah Morgan (2016)

Fundamenta Mathematicae

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For a space Z let 𝒦(Z) denote the partially ordered set of all compact subspaces of Z under set inclusion. If X is a compact space, Δ is the diagonal in X², and 𝒦(X²∖Δ) has calibre (ω₁,ω), then X is metrizable. There is a compact space X such that X²∖Δ has relative calibre (ω₁,ω) in 𝒦(X²∖Δ), but which is not metrizable. Questions of Cascales et al. (2011) concerning order constraints on 𝒦(A) for every subspace of a space X are answered.

Notes on monotone Lindelöf property

Ai-Jun Xu, Wei-Xue Shi (2009)

Czechoslovak Mathematical Journal

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We provide a necessary and sufficient condition under which a generalized ordered topological product (GOTP) of two GO-spaces is monotonically Lindelöf.

Monotone meta-Lindelöf spaces

Yin-Zhu Gao, Wei-Xue Shi (2009)

Czechoslovak Mathematical Journal

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In this paper, we study the monotone meta-Lindelöf property. Relationships between monotone meta-Lindelöf spaces and other spaces are investigated. Behaviors of monotone meta-Lindelöf G O -spaces in their linearly ordered extensions are revealed.