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Filter topologies on MV-algebras II

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Abstract

We show in this paper that the filter topology on an MV-chain is precisely the order topology when the filter is non-principal and has an infimum in the MV-chain. Then, we show that for an arbitrary MV-algebra A which is complete, the canonical monomorphism h of A into its subdirect product must be a continuous mapping. As a result, we give a sufficient condition for a complete MV-algebra equipped with the filter topology to be Hausdorff.

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Authors and Affiliations

  1. School of Mathematics and System Sciences, Beihang University, Beijing, 100191, China

    Sifan Wu, Wei Luan & Yichuan Yang

Authors
  1. Sifan Wu
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  2. Wei Luan
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  3. Yichuan Yang
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Corresponding author

Correspondence to Yichuan Yang.

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The authors declare that they have no conflict of interest.

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Communicated by A. Di Nola.

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Y. Yang: supported by supported by CNNSF (Grant No. 11771004).

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Wu, S., Luan, W. & Yang, Y. Filter topologies on MV-algebras II. Soft Comput 24, 3173–3177 (2020). https://doi.org/10.1007/s00500-020-04682-5

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  • DOI: https://doi.org/10.1007/s00500-020-04682-5

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