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The upgrade of topological group based on a new hyper-topology

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Fuzzy Information and Engineering

Abstract

Wang et al [1] have put forward the problem of upgrade of topology and obtained a series of systematic theories and applicable results. Li et al [2] have put forwarded the problem of upgrade of group and also obtained a series of results. Consequently, the problem of upgrade of mathematic structure has drawn more attention of researchers. However, for the work to upgrade topology and group at the same time, little progress has been made although there are someone studying on it. Based on a kind of intuitive convergent way, the paper has proposed a new hyper-topology and upgraded two mathematic structures of topological group to power set and fuzzy power set respectively. It has proved that multiplication and contradiction operations continues in the new hyper-topology after upgrading and a series of results are obtained creating hyper-topological group and fuzzy hyper-topological group. Accordingly, hyper-topological group and fuzzy hyper-topological group can be created, obtaining a breakthrough to upgrade topological group to its power set and fuzzy power set.

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Authors and Affiliations

  1. School of Mathematics and Information Sciences, Guangzhou University, Guangzhou, 510006, P.R.China

    Yu-bin Zhong

  2. School of Mathematics Sciences, Beijing Normal University, Beijing, 100875, P.R.China

    Hong-xing Li

  3. College of Electronic and Information Engineering, Dalian University of Technology, Dalian, P.R.China

    Hong-xing Li

Authors
  1. Yu-bin Zhong
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  2. Hong-xing Li
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Corresponding authors

Correspondence to Yu-bin Zhong or Hong-xing Li.

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Zhong, Yb., Li, Hx. The upgrade of topological group based on a new hyper-topology. Fuzzy Inf. Eng. 3, 137–146 (2011). https://doi.org/10.1007/s12543-011-0072-y

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  • DOI: https://doi.org/10.1007/s12543-011-0072-y

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