We define and discuss the notions of additivity and idempotency for neighbourhood and interior operators. We then propose an order-theoretic description of the notion of convergence that was introduced by D. Holgate and J. Šlapal with the help of these two properties. This will provide a rather convenient setting in which compactness and completeness can be studied via neighbourhood operators. We prove, among other things, a Frolík-type theorem with the introduction of reflecting morphisms.

中文翻译：

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邻域算子：可加性、幂等性和收敛性

我们定义并讨论了邻域和内部算子的可加性和幂等性的概念。然后，我们提出了 D. Holgate 和 J. Šlapal 在这两个属性的帮助下引入的收敛概念的顺序理论描述。这将提供一个相当方便的设置，可以通过邻域算子研究紧凑性和完整性。我们证明了一个 Frolík 型定理，其中引入了反射态射。