Syndetic equicontinuity and uniform rigidity without equicontinuity in minimal systems

Huang, Kolyada and Zhang asked whether every syndetically equicontinuous uniformly rigid system is equicontinuous. We answer this question negatively, even for minimal systems. We construct a minimal uniformly rigid system as an almost one-to-one extension of an odometer. The extension is syndetically equicontinuous but not equicontinuous, and the odometer is its maximal equicontinuous factor.