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2020 | 149 | 92-109
Article title

R-Countability Axioms

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EN
Abstracts
EN
In this article, we use the concept of regular open sets to define a generalization of the countability axioms; namely regular countability axioms, and they are denoted by r-countability axioms. This class of axioms includes r-separable spaces, r-first countable spaces, r-Lindelöf spaces, r-𝜎-compact spaces and r-second countable spaces. We investigate their fundamental properties, and study the implication of the new axioms among themselves and with the known axioms. Moreover, we study the hereditary properties for r-countability axioms, also we consider some related functions in terms of r-open sets, which preserve these spaces. Finally, we prove that in regular space r-countability axioms and countability axioms are equivalent, while in locally compact T_2 space, the spaces: Lindelöf, r- Lindelöf, 𝜎-compact and r-𝜎-compact are all equivalent.
Year
Volume
149
Pages
92-109
Physical description
Contributors
  • Mathematics Department, Higher Institute of Science and Technology, Tripoli, Libya
  • Mathematics Department, Tripoli University, Tripoli, Libya
References
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Document Type
article
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.psjd-4c79d218-1a8c-45af-96ba-32d66ecd0431
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