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

Abstract

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