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

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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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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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  1. Department of Liberal Arts, Japan Coast Guard Academy, 5-1 Wakaba-cho, Kure, Hiroshima, 737-8512, Japan

    Masato Fujita

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  1. Masato Fujita
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Correspondence to Masato Fujita.

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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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