{"id":"palomar/PALOMAR-2026-10-07-000008","url":"https://github.com/Arthur742Ramos/Math-Formalization/tree/8b802e2f62a31b08276a67021cd40f6941c5c256/topology/order-arcs","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-07-000008-v1.json","repo":"https://github.com/Arthur742Ramos/Math-Formalization","tags":["math.GN","msc:54F15","msc:54B20","topology","continua","order-theory"],"score":0,"title":"Order Arcs Between Subcontinua","trust":"high","domain":"math.GN","source":"palomar","authors":["Arthur Freitas Ramos","David Barros Hulak","Ruy Jose Guerra Barretto de Queiroz"],"reviews":0,"subject":"math.GN","summary":"Properly nested nonempty compact connected subsets A and B of a compact metric space are the endpoints of a continuous embedded interval of nonempty compact connected subsets, strictly increasing under inclusion. The ambient space need not be connected.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-07","reactions":{},"formalized":true,"formalizes":[{"title":"Hyperspaces of a continuum","identifier":"https://doi.org/10.1090/S0002-9947-1942-0006505-8","relationship":"adapts"}]}