In topological spaces, the relation of extended contact is a ternary relation that holds between regular closed subsets A, B and D if the intersection of A and B is included in D. The algebraic counterpart of this mereotopological relation is the notion of extended contact algebra which is a Boolean algebra extended with a ternary relation. In this paper, we are interested in the relational representation theory for extended contact algebras. In this respect, we study the correspondences between point-free and point-based models of space in terms of extended contact. More precisely, we prove new representation theorems for extended contact algebras.

中文翻译：

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扩展接触代数的关系表示定理

在拓扑空间中，如果 A 和 B 的交集包含在 D 中，则扩展接触的关系是在规则闭合子集 A、B 和 D 之间成立的三元关系。这种分体拓扑关系的代数对应物是扩展接触代数的概念这是一个用三元关系扩展的布尔代数。在本文中，我们对扩展接触代数的关系表示理论感兴趣。在这方面，我们在扩展接触方面研究了无点和基于点的空间模型之间的对应关系。更准确地说，我们证明了扩展接触代数的新表示定理。