{"id":"palomar/PALOMAR-2026-10-29-000037","url":"https://github.com/Arthur742Ramos/Math-Formalization/tree/5c3ff130a8d8ecf6f4021f72ad6241dcf15703cd/topology/auslander-yorke-dichotomy","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-29-000037-v1.json","repo":"https://github.com/Arthur742Ramos/Math-Formalization","tags":["math.DS","math.GN","msc:37B05","msc:37B02"],"score":0,"title":"Auslander–Yorke dichotomy for minimal metric maps","trust":"high","domain":"math.DS","source":"palomar","authors":["Arthur Freitas Ramos","David Barros Hulak","Ruy Jose Guerra Barretto de Queiroz"],"reviews":0,"subject":"math.DS","summary":"For a continuous map of a metric space with every forward natural orbit dense, either the map is sensitive in the open-set pair sense or its natural iterate family is equicontinuous at every point. Stable open sets are propagated using dense orbits and finite early-time continuity. On nonempty spaces nonsensitivity is equivalent to equicontinuity; no compactness or uniform-equicontinuity assertion is required.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-29","reactions":{},"formalized":true}