Chinese Quarterly Journal of Mathematics ›› 2012, Vol. 27 ›› Issue (2): 246-253.

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Prime MP-filter Spaces of Fuzzy Implication Algebras

  

  1. 1. Department of Elementary Education, Chifeng University 2. Department of Mathematics Science, Yangzhou University

  • Received:2010-09-09 Online:2012-06-30 Published:2023-03-29
  • About author:LIU Chun-hui(1982-), male, native of Chifeng, Inner Mongolia, a lecturer of Chifeng University, M.S.D., engages in Domain theory, non-classical mathematical logic and topology; XU Luo-shan(1957-), male, native of Yangzhou, Jiangsu, a professor of Yangzhou University, Ph.D., engages in Domain theory, non-classical logic and topology.
  • Supported by:
    Supported by the NSF of China(10371106,60774073)

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Abstract: In this paper, the topological space (PFMP(X), T) based on prime MP-filters of a lattice FI-algebra X is constructed firstly and we proved that it is a compact T0-space if X with condition (P). Secondly, we restricted T to the set of all maximal MP-filters MFMP(X) of X and concluded that (PFMP(X), T |(PFMP(X))) is a compact T2 space if X with conditions (P) and (S).


Key words: Fuzzy implication algebra, MP-filter, prime MP-filter, topological space

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