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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Acknowledgements
The author appreciates an anonymous referee for his/her insightful comments. He/she suggested a shorter proof of the main theorem than the original one.
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Fujita, M. Definable Tietze extension property in o-minimal expansions of ordered groups. Arch. Math. Logic 62, 941–945 (2023). https://doi.org/10.1007/s00153-023-00875-5
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DOI: https://doi.org/10.1007/s00153-023-00875-5