Michael's selection theorem in general d-minimal structures

Masato Fujita

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arXiv · 2402.14222

Michael's selection theorem in general d-minimal structures

Masato Fujita

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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 $\mathcal F=(F,<,+,\cdot,0,1,\ldots)$. 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.

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BibTeX RIS

Masato Fujita. 2024-02-22. Michael's selection theorem in general d-minimal structures. https://arxiv.org/abs/2402.14222

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