Submission date: 3 November 2020

Abstract:

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

Mathematics Subject Classification: 03C64

Keywords and phrases:

Full text arXiv 2011.02922: pdf, ps.