Yang Anzhou. Complete Subsets and Idempotent Isotone Self-mappings in a Complete Lattice[J]. Journal of Beijing University of Technology, 1991, 17(1): 70-70.
Citation:
Yang Anzhou. Complete Subsets and Idempotent Isotone Self-mappings in a Complete Lattice[J]. Journal of Beijing University of Technology, 1991, 17(1): 70-70.
Yang Anzhou. Complete Subsets and Idempotent Isotone Self-mappings in a Complete Lattice[J]. Journal of Beijing University of Technology, 1991, 17(1): 70-70.
Citation:
Yang Anzhou. Complete Subsets and Idempotent Isotone Self-mappings in a Complete Lattice[J]. Journal of Beijing University of Technology, 1991, 17(1): 70-70.
Complete Subsets and Idempotent Isotone Self-mappings in a Complete Lattice
We obtained following theorem: Let(L, ≤) be a complete lattice,S⫅L. S is a complete lattice under ≤ if and only if there is an idempotent isotone self-mapping φ of L such that Fix(φ)=x∈L: φ(x)=x=range(φ)=φ(x): x∈L=S.
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