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Soft Computing

, Volume 23, Issue 24, pp 12951–12960 | Cite as

The properties of \(\models \)-filters of a topological system

  • Tao Wu
  • Bin ZhaoEmail author
Foundations
  • 161 Downloads

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.

Keywords

Topological systems BL-algebra Maximal \(\models \)-filters 

Notes

Acknowledgements

This research is supported by a Grant of National Natural Science Foundation of China (11531009).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of authors.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematics and Information ScienceShaanxi Normal UniversityXi’anChina

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