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: | , |
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
Hindawi Limited
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/a4f7d24319104aa29faa39878718a4cf |
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| Sumario: | 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. |
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