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Remarque sur les treillis complets pseudo-complémentés. (Remark on complete pseudocomplemented lattices). (French) Zbl 0687.06004

Let \({\mathcal L}\) be a complete pseudo-complemented lattice and let \(\alpha\) be a mapping from a set S into \({\mathcal L}\). For \(X\subseteq S\) define \(a(X)=(C\circ g\circ i\circ f)(X)\), where \(f(X)=V\alpha (X)\), i is the identity mapping from the dual lattice \({\mathcal L}^ d\) onto \({\mathcal L}\), \(g(x)=\alpha^{-1}([0,x])\) for \(x\in {\mathcal L}\) and \(CX=S\setminus X\). It is proved that the set of all \(X\subseteq S\) such that \(a(X)=X\) is closed under union and complementation.
Reviewer: V.N.Salij

MSC:

06B23 Complete lattices, completions
06C15 Complemented lattices, orthocomplemented lattices and posets
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