Idempotent bonding relations are nontrivial if and only if they satisfy condition Gamma

A relation $f\subseteq X^2$ satisfies condition $Γ$ if there exist distinct $x,y\in X$ with $\langle x,x\rangle ,\langle x,y\rangle ,\langle y,y\rangle \in f$. The authors improve a previous result by characterizing nontrivial idempotent bonding relations on compact Hausdorff spaces as those satisfying condition $Γ$.

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