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Pre-derived operators, pre-difference derived operators and pre-topologies

YANG Xiao-fei, LI Sheng-gang*   

  1. College of Mathematics and Information Sciences, Shaanxi Normal University,Xi'an 710062, Shanxi, China
  • Received:1900-01-01 Revised:1900-01-01 Online:2006-10-24 Published:2006-10-24
  • Contact: YANG Xiao-fei

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Abstract: The concepts of pre-derived operator and pre-difference derived operator were introduced. It was proved that, for a given set X, appropriate order relations≤can be defined on PD(X) (the set of all pre-derived operators on X) and PDD(X) (the set of all pre-difference derived operators on X), respectively, such that both (PD(X), ≤) and (PDD(X), ≤) are complete lattices which are isomorphic to (PT(X))(the set of all pre-topologies on the set X).

Key words: complete lattice , pre-topology, difference derived operater, pre-difference derived operater, derived operater, pre-derived operater

CLC Number: 

  • O189.1
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