In a topological space (X, T) at most 7 distinct sets can be constructed from a set A ∈ 2~X by successive applications of the closure and interior operation in any order. If sets so constructed are called closure-interior relatives of A, then for each topological space (X, T) with |X| ≥ 7 there exists a set with 7 closure-interior relatives; for |X| < 7, however, 7 closure-interior relatives of a set cannot co-exist. Using relation algebra and the RELVIEW tool we compute all closure-interior relatives for all topological spaces with less than 7 points. From these results we obtain that for all finite topological spaces (X, T) the maximum number of closure-interior relatives of a set is |X|, with one exception: For the indiscrete topology T = {0,X} on a set X with |X| = 2 there exist two sets which possess |X| + 1 closure-interior relatives.
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机译：在最多7个拓扑空间（X，T）中，可以通过以任何顺序的闭合和内部操作的连续应用来构造由设置的封闭和内部操作的设定A≠2〜X结构。如果设置如此构造的被称为封闭内部亲属，那么为每个拓扑空间（x，t）与| x | ≥7有7个封闭内部亲属的设定; for | x | <7，然而，设定的7个闭合内部亲属不能共存。使用关系代数和relview工具，我们计算所有封闭内部亲属的所有拓扑空间，拓扑空间少于7分。从这些结果来看，我们获得所有有限拓扑空间（x，t）集合的闭合内部亲属的最大数量为| x |，其中一个例外：对于一组上的Indiscrete拓扑T = {0，x} x与| x | = 2有两套拥有| x | + 1个关闭内部亲属。
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