论文标题
一些关于反题学空间的评论
Some remarks on anti-topological spaces
论文作者
论文摘要
本文致力于一般性的反亲戚空间。这些结构最初是由2021年的Hahin，Kargın和M.Yücel提出的。我们分析了它们的基本定义，显示了其一些细微之处和含义。因此获得的框架用于研究某些基本拓扑概念的抗辩解释。例如，我们讨论了内部和封闭的想法，并在门空间上显示了一些结果。此外，我们引入了两种非等效类型的连续性。最后，我们研究了密度和无处密度的概念。最后，我们给出了一些关于反探针空间模态逻辑的初步建议。值得注意的是，该论文在基础和弱空间中包含一些其他评论。它们可能被认为是对文献中一些早期结果的澄清或纠正。
This paper is devoted to a general presentation of anti-topological spaces. These structures have been initially proposed by Şahin, Kargın and M. Yücel in 2021. We analyse their basic definition, showing some of its subtleties and implications. The framework thus obtained is used to investigate anti-topological interpretation of some basic topological notions. For example, we discuss the idea of interior and closure and we show some results on door spaces. Moreover, we introduce two non-equivalent types of continuity. Finally, we investigate the idea of density and nowhere density. Finally, we give some preliminary suggestions concerning the modal logic of anti-topological spaces. It is noteworthy that the paper contains some additional remarks on infra-topological and weak spaces. They may be considered as a clarification or correction of some earlier results present in literature.
