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$C_σ$-Unique Dcpos: Intrinsic Characterizations and Counterexamples
A dcpo \(D\) is called \(C_σ\)-unique if for every dcpo \(Q\), \( Γ(D)\cong Γ(Q) \) implies \( D\cong Q, \) where \(Γ(D)\) denotes the lattice of Scott-closed subsets of \(D\). We give an intrinsic characterization of \(C_σ\)-uniqueness in terms of Skula-density and Scott closure, identifying precis
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