Definition 17.10.553FB52FA474A3

Definition 17.10.55.3FB52FA474A3 Let $E$ be a set. A pre-rooftop structure on $E$ is a binary operator $\land :E\times E\rightarrow E$, satisfying the following axioms: For $x,y,z\in E$,

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   $x\land y=y\land x$.

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   $(x\land y)\land z=x\land (y\land z)$.

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   $x\land x=x$.

We call $(E,\land )$ a pre-rooftop space.