Definable Tietze extension property in o-minimal expansion of ordered group

Abstract

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

arXiv commentIncluded as an appendix of the updated arXiv:2010.02420