Submission date: 22 February 2024

Abstract:

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.

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Full text arXiv 2402.14222: pdf, ps.