D-countability axioms

• Authors: Khadiga Ali Arwini , Amel Emhemed Kornas
• Languages of publication: EN

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.

Keywords

EN

Countability axioms; sequential spaces; 𝛿-compact spaces

Discipline

• PHYSICS: PHYSICS

• Publisher: Scientific Publishing House „DARWIN”
• Journal: World Scientific News
• Year: 2020
• Volume: 143
• Pages: 28-38

Contributors

author

Khadiga Ali Arwini

• Department of Mathematics, Tripoli University, Tripoli, Libya

author

Amel Emhemed Kornas

• Department of Mathematics, Higher Institute of Science and Technology, Tripoli, Libya

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• Document Type: article