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 $\mathcal{F}=(F,<,+,\cdot ,0,1,\dots )$. We also show that we can choose a definable continuous selection $f$ of a lower semi-continuous map $T:E\rightrightarrows F$ so that $f(x)$ is contained in the interior of $T(x)$ when the interior is not empty.