Michael's selection theorem in general d-minimal structures

Thamrongthanyalak demonstrated a definable version of Michael's selection theorem in d-minimal expansions of the real field. We generalize this result to the case in which the structures are d-minimal expansions of ordered fields F=(F,<,+,·,0,1,…). We also show that we can choose a definable continuous selection f of a lower semi-continuous map T:E F so that $f(x)$ is contained in the interior of $T(x)$ when the interior is not empty.