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Reflectional Topology in Residuated Lattices

Author

Listed:
  • F. Forouzesh

    (Faculty of Mathematics and computing, Higher Education Complex of Bam, Iran2Department of Pure Mathematics, Shahid Bahonar University of Kerman, Iran)

  • S. N. Hosseini

    (Faculty of Mathematics and computing, Higher Education Complex of Bam, Iran1Faculty of Mathematics and computing, Higher Education Complex of Bam, Iran)

Abstract

In this paper, we introduce soaker filters in a residuated lattice, give some characterizations and investigate some properties of them. Then we define a topology on the set of all the soaker filters, which we call reflectional topology, show it is an Alexandrov topology and give a basis for it. We introduce the notion of join-soaker filters and prove that when the residuated lattice is a join-soaker filter, then the reflectional topology is compact. We also give a characterization of connectedness of the reflectional topology. Finally, we prove the reflectional topology is T0, give necessary and sufficient conditions under which it is T1 and prove that being T2 is equivalent to being T1. Several illustrative examples are given.

Suggested Citation

  • F. Forouzesh & S. N. Hosseini, 2020. "Reflectional Topology in Residuated Lattices," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 16(03), pages 593-608, November.
    • Handle: RePEc:wsi:nmncxx:v:16:y:2020:i:03:n:s1793005720500362
    DOI: 10.1142/S1793005720500362
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