PomeDefinition 17.10.56.602E107F6064 Let $(E,d)$ be a metric space. A pre-rooftop structure on $(E,d)$ is a pre-rooftop structure $\land $ on $E$. We say $(E,d,\land )$ is a pre-rooftop metric space.
A rooftop structure on $(E,d)$ is a pre-rooftop structure $\land $ on $E$ such that
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\begin{equation} d(x\land z,y\land z)\leq d(x,y),\quad \forall x,y,z\in E. \end{equation}
We call $(E,d,\land )$ a rooftop metric space.
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