{"id":"palomar/PALOMAR-2026-10-07-000003","url":"https://github.com/Arthur742Ramos/Math-Formalization/tree/53be25d26551d18b006d3a625fc5b145cc73cebd/topology/composants","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-07-000003-v1.json","repo":"https://github.com/Arthur742Ramos/Math-Formalization","tags":["math.GN","msc:54F15","msc:54D05","msc:54D30","continuum-theory","general-topology","indecomposable-continua"],"score":0,"title":"Alexandroff Property of Metric Indecomposable 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":"Todorov–Valov Theorem 3.3: for two disjoint closed sets with nonempty interiors in a metric indecomposable continuum, one open cover obstructs every separator map onto every nonempty compact connected Hausdorff target. The classical composant properties remain as foundations.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-07","reactions":{},"formalized":true,"formalizes":[{"title":"Generalized Cantor manifolds and indecomposable continua","identifier":"https://www.jstage.jst.go.jp/article/qagt/30/2/30_93/_pdf/-char/en","relationship":"adapts"},{"title":"Indecomposable and Chainable Continua","identifier":"https://etd.auburn.edu/bitstream/handle/10415/1827/Sturm-ThesisComplete.pdf?isAllowed=y&sequence=1","relationship":"adapts"}]}