A characterization of the countable paracompactness for products of ordinals

Hirata, Yasushi; Yajima, Yukinobu

doi:10.1016/j.topol.2020.107325

Cited by 2 publications

(1 citation statement)

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“…In general topology, several topological properties are not finitely productive, such as paracompactness, strong paracompactness, Lindelöfness, and metacompactness. e area of research regarding the problem "What conditions on (Y, σ) and (Z, δ) to insure that their product has property P"is still hot [38][39][40][41][42][43][44][45]. e second goal of this paper is to introduce several product theorems concerning metacompactness.…”

Section: Introductionmentioning

confidence: 99%

Theta Omega Topological Operators and Some Product Theorems

Ghour

El-Issa

2021

Mathematical Problems in Engineering

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We introduce and investigate the concepts of θ ω -limit points and θ ω -interior points, and we use them to introduce two new topological operators. For a subset B of a topological space Y , σ , denote the set of all limit points of B (resp. θ -limit points of B , θ ω -limit points of B , interior points of B , θ -interior points of B , and θ ω -interior points of B ) by D B (resp. D θ B , D θ ω B , Int B , Int θ B , and Int θ ω B ). Several results regarding the two new topological operators are given. In particular, we show that D θ ω B lies strictly between D B and D θ B and Int θ ω B lies strictly between Int θ B and Int B . We show that D B = D θ ω B (resp. Cl θ B = Cl θ ω B and D B = D θ ω B = D θ B ) for locally countable topological spaces (resp. antilocally countable topological spaces and regular topological spaces). In addition to these, we introduce several product theorems concerning metacompactness.

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