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

中文翻译：

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更多有关-拓扑空间中的闭集

本文的目的是提出和研究的拓扑性质-衍生-边境，-边，-基于的概念一组外部-开集。然后，我们通过使用-开放集和-封闭概念引入新的分离公理（即和）。的空间（相应的，）是严格的空间之间（分别，）和（相应的，）。此外，我们提出了-内核和-收敛到一点，并讨论-闭包和-内核之间有趣的特性的表征。最后，研究了弱空间的几种性质。