Relational representation theorems for extended contact algebras. (English) Zbl 07424395
Summary: 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.
MSC:
| 03-XX | Mathematical logic and foundations |
Keywords:
mereotopology; point-free theory of space; contact algebras; extended contact algebras; regular closed subsets; relational representationReferences:
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