Definably connected nonconnected sets

Abstract

Abstract We give an example of a structure \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal R$\end{document} on the real line, and a manifold M definable in \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {R}$\end{document} , such that M is definably connected but is not connected.