The aim of this work is to define some concepts on supra topological spaces using supra preopen sets and investigate main properties. We started this paper by correcting some results obtained in previous study and presenting further properties of supra preopen sets. Then, we introduce a concept of supra prehomeomorphism maps and discuss its main properties. After that we explore the concepts of supra limit and supra boundary points of a set with respect to supra preopen sets and examine their behaviours on the spaces that possess the difference property. Finally, we formulate the concepts of supra pre--spaces and give completely descriptions for each one of them. In general, we study their main properties in detail and show the implications of these separation axioms among themselves as well as with -space with the help of some interesting examples.

中文翻译：

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Supra Preopen集的一些应用

这项工作的目的是使用超前开放集定义超拓扑空间上的一些概念并研究主要属性。我们通过更正先前研究中获得的一些结果并介绍上述预开放集的进一步性质来开始本文。然后，我们介绍了超前同胚图的概念，并讨论了它的主要特性。之后，我们针对超预开集探索了一个集合的超极限和超边界点的概念，并检验了它们在具有差异性质的空间上的行为。最后，我们制定的超前期的概念-空间并给出其中每一个的完整描述。在一般情况下，我们详细研究了它们的主要性能及显示彼此之间以及与这些分离性的影响-有一些有趣的例子帮助的空间。