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2020 | 143 | 28-38
Article title

D-countability axioms

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Abstracts
EN
In this paper, we introduce new axioms using the concepts of the countability axioms via dense sets, namely dense countability axioms and they are denoted by D-countability axioms, where a topological space is called D-sequential (D-separable, D-first countable, D-Lindelöf, D-𝛿-compact or D-second countable) space if it has a dense sequential (separable, first countable, Lindelöf, 𝛿-compact or second countable) subspace. We prove that D-separable spaces and D-second countable spaces are equivalent to separable spaces. Moreover, we study some properties of D-countability axioms; as their subspaces and their continuous images. In addition, we provide some inter-relations between D-countability axioms and countability axioms through some examples.
Discipline
Year
Volume
143
Pages
28-38
Physical description
Contributors
  • Department of Mathematics, Tripoli University, Tripoli, Libya
  • Department of Mathematics, Higher Institute of Science and Technology, Tripoli, Libya
References
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Document Type
article
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.psjd-80fbebfb-1835-4fbb-8316-4ccde238b141
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