Theta Omega Topological Operators and Some Product Theorems

We introduce and investigate the concepts of θω-limit points and θω-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, θω-limit points of B, interior points of B,...

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Autores principales:	Samer Al Ghour, Salma El-Issa
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Engineering (General). Civil engineering (General) TA1-2040 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/a4f7d24319104aa29faa39878718a4cf
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id	oai:doaj.org-article:a4f7d24319104aa29faa39878718a4cf
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spelling	oai:doaj.org-article:a4f7d24319104aa29faa39878718a4cf2021-11-29T00:55:32ZTheta Omega Topological Operators and Some Product Theorems1563-514710.1155/2021/6438053https://doaj.org/article/a4f7d24319104aa29faa39878718a4cf2021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/6438053https://doaj.org/toc/1563-5147We introduce and investigate the concepts of θω-limit points and θω-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, θω-limit points of B, interior points of B, θ-interior points of B, and θω-interior points of B) by DB (resp. DθB, DθωB, IntB, IntθB, and IntθωB). Several results regarding the two new topological operators are given. In particular, we show that DθωB lies strictly between DB and DθB and IntθωB lies strictly between IntθB and IntB. We show that DB=DθωB (resp. ClθB=ClθωB and DB=DθωB=DθB) 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.Samer Al GhourSalma El-IssaHindawi LimitedarticleEngineering (General). Civil engineering (General)TA1-2040MathematicsQA1-939ENMathematical Problems in Engineering, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Engineering (General). Civil engineering (General) TA1-2040 Mathematics QA1-939
spellingShingle	Engineering (General). Civil engineering (General) TA1-2040 Mathematics QA1-939 Samer Al Ghour Salma El-Issa Theta Omega Topological Operators and Some Product Theorems
description	We introduce and investigate the concepts of θω-limit points and θω-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, θω-limit points of B, interior points of B, θ-interior points of B, and θω-interior points of B) by DB (resp. DθB, DθωB, IntB, IntθB, and IntθωB). Several results regarding the two new topological operators are given. In particular, we show that DθωB lies strictly between DB and DθB and IntθωB lies strictly between IntθB and IntB. We show that DB=DθωB (resp. ClθB=ClθωB and DB=DθωB=DθB) 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.
format	article
author	Samer Al Ghour Salma El-Issa
author_facet	Samer Al Ghour Salma El-Issa
author_sort	Samer Al Ghour
title	Theta Omega Topological Operators and Some Product Theorems
title_short	Theta Omega Topological Operators and Some Product Theorems
title_full	Theta Omega Topological Operators and Some Product Theorems
title_fullStr	Theta Omega Topological Operators and Some Product Theorems
title_full_unstemmed	Theta Omega Topological Operators and Some Product Theorems
title_sort	theta omega topological operators and some product theorems
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/a4f7d24319104aa29faa39878718a4cf
work_keys_str_mv	AT sameralghour thetaomegatopologicaloperatorsandsomeproducttheorems AT salmaelissa thetaomegatopologicaloperatorsandsomeproducttheorems
_version_	1718407789063176192

Theta Omega Topological Operators and Some Product Theorems

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