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Some New Variants of Relative Regularity via Regularly Closed Sets

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  • Sehar Shakeel Raina
  • A. K. Das
  • Frédéric Mynard

Abstract

Every topological property can be associated with its relative version in such a way that when smaller space coincides with larger space, then this relative property coincides with the absolute one. This notion of relative topological properties was introduced by Arhangel’skii and Ganedi in 1989. Singal and Arya introduced the concepts of almost regular spaces in 1969 and almost completely regular spaces in 1970. In this paper, we have studied various relative versions of almost regularity, complete regularity, and almost complete regularity. We investigated some of their properties and established relationships of these spaces with each other and with the existing relative properties.

Suggested Citation

  • Sehar Shakeel Raina & A. K. Das & Frédéric Mynard, 2021. "Some New Variants of Relative Regularity via Regularly Closed Sets," Journal of Mathematics, Hindawi, vol. 2021, pages 1-6, May.
    • Handle: RePEc:hin:jjmath:7726577
    DOI: 10.1155/2021/7726577
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