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- W2809241422 abstract "Properties (A) and (B) were introduced by Chase and Gruenhage in 2016. Let X be a topological space and let P(X) be the collection of all pairs (x,U) where x∈X and U is an open neighborhood of x in X. A space X has property (A) (resp., property (B)) if to each (x,U)∈P(X), one can assign an open set V(x,U) such that x∈V(x,U)⊂U and such that for any collection {(xα,Uα):α∈A}⊂P(X), either ⋂α∈AV(xα,Uα)=∅, or there exists a finite set A′⊂A such that for each α∈A there exists β∈A′ with V(xα,Uα)⊂Uβ (resp., {xα:α∈A}⊂⋃β∈A′Uβ). We discuss properties of property (A) ((B)) and get the following conclusions: If a regular topological space X has caliber ω1 and satisfies property (A), then X is a second countable metrizable space. If X is a GO-space, then X has property (A) ((B)) if and only if the closed linearly ordered extension X⁎ of X has property (A) ((B)). If X is a scattered GO-space which satisfies property (B), then X is monotonically metacompact. If L is a monotonically metacompact GO-space and Y is a convex subspace of L, then Y is monotonically metacompact. If (X,τ,<) is a GO-space such that X∖Iτ has property (A) ((B)), then X has property (A) ((B)), where Iτ={x∈X:{x} is open in X}. If (X,τ,<) is a GO-space whose underlying LOTS (X,λ,<) has a σ-closed-discrete dense subset, then X is monotonically metacompact if and only if X∖Iτ is monotonically countably metacompact, where Iτ={x∈X:{x} is open in X}." @default.
- W2809241422 created "2018-06-29" @default.
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- W2809241422 date "2018-08-01" @default.
- W2809241422 modified "2023-10-16" @default.
- W2809241422 title "A study on monotonically metacompact and property (A) ((B))" @default.
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- W2809241422 doi "https://doi.org/10.1016/j.topol.2018.06.003" @default.
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