Definition. The lifting operator for cpos [dt-003K]Liam O'Connor The lifting operator (\cdot )_\bot adds a new \bot value to a cpo. That is, for a cpo X: X_\bot = X \cup \{\bot \} \quad \text {(where $\bot \notin X$)} For all x \in X (including \bot _X), our new bottom value \bot \sqsubseteq x.