{"id":"palomar/PALOMAR-2026-10-23-000001","url":"https://github.com/Arthur742Ramos/Math-Formalization/tree/ea2e84471cdd230fd133a9e2e3b0dfc25e1a7f0f/topology/cantor-space-characterization","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-23-000001-v1.json","repo":"https://github.com/Arthur742Ramos/Math-Formalization","tags":["math.GN","math.LO","msc:54F65","msc:54D30","msc:03E15","general-topology","cantor-space","formalization"],"score":0,"title":"Brouwer characterization of Cantor space","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":"A topological space is homeomorphic to Cantor space, the countable product of discrete Boolean spaces, if and only if it is nonempty, compact, metrizable, has a basis of clopen sets, and has no isolated points. A full binary clopen scheme decides an enumerated basis one element at each depth. Its point-address map is continuous; compact nested intersections realize every binary branch, and basis decisions separate points. A continuous bijection from a compact space to the Hausdorff Cantor space is a homeomorphism. This formalizes a classical theorem of Brouwer; no mathematical novelty or…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-23","reactions":{},"formalized":true,"formalizes":[{"title":"Introduction to descriptive set theory","identifier":"https://www.math.mcgill.ca/atserunyan/Teaching_notes/dst_lectures.pdf","relationship":"formalizes"}]}