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Erschienen in:
05.08.2019 | Foundations
The properties of \(\models \)-filters of a topological system
Erschienen in: Soft Computing | Ausgabe 24/2019
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Abstract
The aim of this paper is to build relationships between point logics and logical algebras. Firstly, by modifying Vickers’s Scott open filters, the notion of the \(\models \)-filters of a topological system is introduced. It is proved that the \(\models \)-filters are lattice filters, but the converse is not true. Secondly, the concrete forms of infimum, supremum and implication of the set of all \(\models \)-filters are obtained. It is shown that the set of all \(\models \)-filters of a topological system is a (co)frame and a completely distributive lattice. Finally, we prove that the set of all maximal \(\models \)-filters are endowed with two topologies forming a \(T_{2}\) space and a \(T_{1}\) space.