Definable Tietze extension property in o-minimal expansions of ordered groups

Archive for Mathematical Logic 62 (7):941-945 (2023)
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Abstract

The following two assertions are equivalent for an o-minimal expansion of an ordered group $$\mathcal M=(M,<,+,0,\ldots )$$. There exists a definable bijection between a bounded interval and an unbounded interval. Any definable continuous function $$f:A \rightarrow M$$ defined on a definable closed subset of $$M^n$$ has a definable continuous extension $$F:M^n \rightarrow M$$.

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10.1007/s00153-023-00875-5

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References found in this work

A structure theorem for semibounded sets in the reals.Ya'acov Peterzil - 1992 - Journal of Symbolic Logic 57 (3):779-794.
Structure theorems for o-minimal expansions of groups.Mario J. Edmundo - 2000 - Annals of Pure and Applied Logic 102 (1-2):159-181.

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