{"id":"palomar/PALOMAR-2026-10-06-000005","url":"https://github.com/Arthur742Ramos/non-cut-points-lean/tree/b1d0ed0338d098a4c84622828390cc84027df8dc","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-06-000005-v1.json","repo":"https://github.com/Arthur742Ramos/non-cut-points-lean","tags":["math.GN","msc:54D05","msc:54D30","msc:54F15","continuum-theory","general-topology","non-cut-points"],"score":0,"title":"Non-Cut Points of Hausdorff Continua","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":"Every nontrivial compact connected subset of a Hausdorff space contains two distinct points whose individual removals leave connected sets. A compact connected subset containing all non-cut points of a compact connected set equals that set.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-06","reactions":{},"formalized":true,"formalizes":[{"title":"Metric Topology: A First Course","identifier":"https://www.mscsnet.mu.edu/~paul/Paper/4450102text.pdf#page=91","relationship":"formalizes"}]}