id author title date pages extension mime words sentence flesch summary cache txt iajs-2911 Y. Y. Yousif; M.H. Jaber ; M. El Sayed Fibrewise Multi-Perfect Topological Spaces 2023 11 .pdf application/pdf 6897 471 91 A subset π’œ of a topological space (E,Ο„) is named to be upper rigid in E (briefly, U.R.) if for every Fβˆ—.Bβˆ—. β„‘ on E π‘Žπ‘‘ 𝑋+(β„‘) ∩ π’œ = βˆ…, βˆƒπ”˜ ∈ 𝜏 and 𝔽 ∈ β„‘ such that π’œ βŠ‚ π”˜ or equivalently, if for every Fβˆ—.Bβˆ—. β„‘ on E, whenever π’œ ∩ (ad β„‘) = βˆ…, thereafter for some F ∈ β„‘, π’œ ∩ (cl(β„‘)) if for all 𝔽 ∈ β„‘, there is G βŠ† 𝔽 meets𝔔 if π”½βˆ©G β‰  βˆ… for 𝑒v𝑒ry 𝔽 ∈ β„‘ and G ∈ 𝔔. Definition 1.10. cache/iajs-2911.pdf txt/iajs-2911.txt