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

Yu-bin Zhong () and Hong-xing Li ()
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Yu-bin Zhong: Guangzhou University
Hong-xing Li: Beijing Normal University

Fuzzy Information and Engineering, 2011, vol. 3, issue 2, 137-146

Abstract: 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.

Keywords: Upgrade; Power set; Fuzzy power set; Power group; Hyper-topological group; Fuzzy hyper-topological group (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s12543-011-0072-y

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