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.