2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/107725A random dense countable set is characterized (in distribution) by independence and stationarity. Two examples are `Brownian local minima' and `unordered infinite sample'. They are identically distributed. A framework for such concepts, proposed here, includes a wide class of random equivalence classes.40 pages. Supersedes math.PR/0508414 and math.PR/0511011ProbabilityBrownian local minima, random dense countable sets and random equivalence classestext