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More on Dα-Closed Sets in Topological Spaces

Author

Listed:
  • Xiao-Yan Gao
  • Ahmed Mostafa Khalil
  • Sami Ullah Khan

Abstract

The aim of this paper is to present and study topological properties of Dα-derived, Dα-border, Dα-frontier, and Dα-exterior of a set based on the concept of Dα-open sets. Then, we introduce new separation axioms (i.e., Dα−R0 and Dα−R1) by using the notions of Dα-open set and Dα-closure. The space of Dα−R0 (resp., Dα−R1) is strictly between the spaces of α−R0 (resp., α−R1) and g−R0 (resp., g−R1). Further, we present the notions of Dα-kernel and Dα-convergent to a point and discuss the characterizations of interesting properties between Dα-closure and Dα-kernel. Finally, several properties of weakly Dα−R0 space are investigated.

Suggested Citation

  • Xiao-Yan Gao & Ahmed Mostafa Khalil & Sami Ullah Khan, 2021. "More on Dα-Closed Sets in Topological Spaces," Journal of Mathematics, Hindawi, vol. 2021, pages 1-9, April.
    • Handle: RePEc:hin:jjmath:5525739
    DOI: 10.1155/2021/5525739
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