完备格中的完备子集与保序冪等的自映射
Complete Subsets and Idempotent Isotone Self-mappings in a Complete Lattice
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摘要: 证明了:若(L,≤)是完备备格,S⫅S在≤下是完备格的充要条件是存在一个L的保序幂等的自映射φ使得Fix(φ)=x∈L:φ(x)=x=range(φ)=:(φ(x)=x∈L=S。Abstract: 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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